- 1 1-1 Warps
- 2 Left+Right Warping
Several situations can result in warping to level 1-1. When the warp is activated, you'll be dropped from the sky and must flutter 9 times while holding right to survive. If 1-1 is completed, the game will continue on as though you had just beaten the level in which the warp was activated. 1-1 Warps can save 4-5 minutes in total in a speedrun.
Each warp is performed differently depending on the level but they all follow the same general format. The area that Yoshi is sent to when he enters a pipe or screen transition is dependent on where Yoshi actually is and not which pipe/screen transition he has entered. Thus, entering a pipe from a different position than normal can result in Yoshi being sent to the coordinates 0,0, the top left corner of the first level, 1-1.
Image explanation: 
In the video, a pipe jump is used to activate the 1-1 Warp, followed by 9 consecutive flutters to survive the fall and complete the level.
How To Do Each Warp
The tutorial video will teach you how to do all the relevant warps for speedrunning.
Enter the secret bonus room near the end of the level. Hold B upon entering the room to begin fluttering. With enough perfect flutters and height gained you can go across the top to either the left or right side to activate the 1-1 Warp. 
Enter the pipe that's next to the locked door (screen 2). Hug and face the wall on the right and begin aiming an egg. Shortly after the Piro Dangle enemy flames up, jump to the left and run into it to get hit. Then, quickly move back to the right. Wait for Baby Mario to touch the wall and then jump up (where you came in from). If you are high enough when you reclaim Baby Mario, the 1-1 Warp will activate. 
At the end of the first cave, do a series of perfect jumps on the yellow moving platform to keep the screen from scrolling up. This will allow you to enter the screen transition from higher than normal to activate the 1-1 Warp. 
Alternate warp: 
This level has 2 different ways of activating the 1-1 Warp!
- Go to the first pipe (the one that leads to the room with Poochy) and do a pipe jump to activate the 1-1 Warp. 
- Jump on the bouncy arrow next to the midring and hold left. After you avoid the wall, hold right to enter the screen transition from above to activate the 1-1 Warp. 
Note: This method is way harder and should be used only as a backup if you fail the first method.
On the second screen just before the horizontal pipe, lure the Boo Blah as close to the pipe as possible. You can use eggs or jump on it's head to skip the animation where it raises it's hands up. When it's right next to the pipe, jump on it and enter the pipe. Entering the pipe this way puts you at a higher position than normal, which activates the 1-1 Warp. 
Note: It is possible that you won't have enough height, even though you were standing on the Boo Blah when entering the pipe.
On the last screen of the level, enter the secret room via beanstalk and hidden !switch. Immediately start fluttering once you enter the room. Hold up to re-enter the pipe and activate the 1-1 Warp. 
Note: You have a 2 frame window to flutter and enter the pipe first try. You can also do perfect flutters to gain height if you don't make it with the first one.
On the second screen, tongue the first monkey then do a small jump off of the post and up-spit the monkey. Jump at the 2nd hanging vine then bounce on the monkey after it jumps onto the vine and do an extended flutter. Keep holding right until you enter the screen transition to activate the 1-1 Warp. 
Note: Make sure to not lose speed when you do the up-spit and avoid the mud, otherwise the monkey may not cooperate with you.
-Information and video coming soon-
Under normal circumstances, this 1-1 Warp cannot be activated, but it exists nonetheless. At the beginning of the last screen of the level, use the free movement feature on the Practice Hack and go just above the bouncy arrow to do the warp. 
Hold left after jumping on the bouncy arrow. If you are far enough to the left, the 1-1 Warp activate. This is by far the easiest warp to execute. 
At the start, grab a shy guy from the pipe but do not eat it, then proceed as normal. You want to have 3 eggs for the warp. Go past the 2nd pipe and stand underneath the stair cloud. Push against the wall and face left, then do 2 neutral egg shots to clear out the spikes. Then, stand on the left side of the pipe, on the first line on the floor, do a small jump and up-spit the shy guy. Begin an up-shot, lock the egg-aiming cursor at the very top, bounce on the shy guy and fall where you cleared out the spikes. Push against the left wall as you fall and do an extended flutter just before the cursor goes off-screen. Keep holding left and aim for the underside of the pipe. Hold up to enter the pipe to activate the 1-1 Warp. 
Note: It is a 2 frame window to do the extended flutter to get into the pipe. If you go too soon, you won't be able to travel far enough left to reach the pipe before bonking your head. If you go too late, you'll either fall to your death or won't have enough height to reach the pipe. This is easily the hardest warp to execute.
In the second to last screen of the level, go to the bonus room. Get hit and then reclaim Baby Mario near the bottom of the screen to activate the 1-1 Warp. This one can be very tricky because you can either enter the bonus room or fall to your death. 
- 1-1: None
- 1-3: None
- 1-4: ~29s
- 1-6: None
- 2-1: ~48s
- 2-4: ~27s
- 2-5: None
- 3-1: ~10s
- 3-7: -coming soon-
- 4-7: ~1s
- 5-4: ~132s or 2m12s (Optimal 5-4 Skip)
- 5-4: ~216s or 3m36s (No 5-4 Skip)
- 6-7: None
Total Possible Time Save:
- ~247s or 4m07s (Optimal 5-4 Skip)
- ~331s or 5m31s (No 5-4 skip)
- 1-1: None
- 1-3: None
- 1-4: ~29s
- 1-6: None
- 2-1: ~48s
- 2-4: ~54s
- 2-5: ~10s
- 3-1: None
- 3-7: -coming soon-
- 4-7: None
- 5-4: ~141s or 2m21s (Optimal 5-4 skip)
- 5-4: ~201s or 3m21s (No 5-4 skip)
- 6-7: None
Note: Warps are only allowed in 100% No Restrictions.
Total Possible Time Save:
- ~282s or 4m42s (Optimal 5-4 skip)
- ~342s or 5m42s (No 5-4 skip)
These warps require an emulator that allows left+right inputs on the same frame or a modded/broken dpad. Left+right warps can cause several interesting effects such as softlocks, glitched levels, severe lag and save file corruption. Different emulators (and different versions/ROMs) may produce different outcomes. Where you're sent to when you do a left+right warp depends on your coin count.
- RAM address for coin count: 7E037B
- RAM addresses for levels: 7E021A and 7E021B
These are based on 2-bytes and the outcomes are believed to be at an amount of ~56k.
The Warp Glitch is the glitch that makes this possible. It works by pressing < and > at the same time in the overworld. When you then start the level, it is determined by the amount of coins you have. The reason why this happens is because the game doesn't expect you to press both directions at once.
So what happens when you press < + >. Well, to start things, there is an address ($36) which is input data. That means if you press > bit 0 and if you press < bit 1 of $36 is set. The game checks every frame if it should move the cursor. It does this by checking if one of the two bits in $36 is set. Since we pressed both at once, both bits will be set and the game will think it has to move the cursor.
Next step is that the game checks where to move the cursor. The overworld data is at $030F for level 1-1, $0310 for level 1-2 to $0319 which is the "SCORE" button and $031A which is the button configuration. It goes on like that (so 2-1 is $031B). If a level is not unlocked the value for its address is 0, if it is however unlocked then the value will be its level number (so 1 for 1-1, 5 for 2-5, 9 for Extra and 12 for button config). Of course 11 and 12 will be always unlocked. So the game takes the current position and adds it with $(17E182+x). Where x is what you pressed (so it's 1 if you pressed >, 2 if you pressed < and 3 if you pressed both at the same time). The game only expects x to be 1 or 2, which is why $(17E182+1) = 0x01 (so + 1 to get the level after the current one), and $(17E182+2) = 0xFF (which will act as -1 to get the level before the current level).
So the game checks if the next level is unlocked (it does this by bitwise ANDing the value with 0x0F), if not it will add another value until it found a level which is unlocked (which is why the cursor goes directly to the "SCORE" button when pressed right and only 1-1 is unlocked). Since we pressed both directions at the same time x is 3 which results in $(17E182+3) = 0x06, which means it will go 6 levels forward every check (which is why the cursor goes to 1-7 when it is unlocked and you try the glitch). So now it checks addresses like: $0315, $031B, $0321 ... until it reaches $037B which happens to be the current coin value and it stops there because coin amount % 0x0F is not 0 (that is the reason something different happens if you try to do the glitch with 0, 16, 32, 48, etc. coins)."
- Masterjun describing the left+right warp in-depth in his TASvideos submission: Super Mario World 2: Yoshi's Island "glitched" in 06:09.03
Test Results For Left+Right Warping By Hyperzoot
All testing was done from a new file and all of the coins were collected in 1-1 unless otherwise stated. Levels on the over-world map glitch out after performing the warp, after completing the level that was warped to and some are just blank and inaccessible. This trick is a good way to bypass levels or go straight to 6-8 in glitched Any% speedruns.
00 - 1-E. Dying here and trying it again results in warping to 1-1 if done again. If 1-E is completed, Yoshi does the animation of taking Baby Mario to 1-2 on the over-world map but 1-1 is not completed. 1-Bonus is unlocked and the 1-E square is glitched. Completing 1-Bonus fixes the over-world map.
01 - 1-1.
02 - 1-2.
03 - 1-3.
04 - 1-4.
05 - 1-5.
06 - 1-6.
07 - 1-7.
08 - 1-8.
09 - 1-E.
10 - 1-Bonus.
11 - The level intro is glitched and the game softlocks.
12 - Tutorial level.
13 - 2-1.
14 - 2-2.
15 - 2-3.
16 - 1-1.
17 - 2-5.
18 - 2-6.
19 - 2-7.
20 - 2-8.
21 - 2-E.
22 - 1-1. The intro is glitched but the level appears normal.
23 - 1-1. The intro is glitched but the level appears normal.
24 - 1-1. The intro is glitched but the level appears normal.
25 - 3-1.
26 - 3-2.
27 - 3-3.
28 - 3-4.
29 - 3-5.
30 - 3-6.
31 - 3-7.
32 - 1-1.
33 - 3-E.
34 - 1-1. The intro is glitched but the level appears normal.
35 - 1-1. The intro is glitched but the level appears normal.
36 - 1-1. The intro is glitched but the level appears normal.
37 - 4-1.
38 - 4-2.
39 - 4-3.
40 - 4-4.
41 - 4-5.
42 - 4-6.
43 - 4-7.
44 - 4-8.
45 - 4-E.
46 - 1-1. The intro is glitched but the level appears normal.
47 - 1-1. The intro is glitched but the level appears normal.
48 - 1-1.
49 - 5-1.
50 - 5-2.
51 - 5-3.
52 - 5-4.
53 - 5-5.
54 - 5-6.
55 - 5-7.
56 - 5-8.
57 - 5-E.
58 - 1-1. The intro is glitched but the level appears normal.
59 - 1-1. The intro is glitched but the level appears normal.
60 - 1-1. The intro is glitched but the level appears normal.
61 - 6-1.
62 - 6-2.
63 - 6-3.
64 - 1-1.
65 - 6-5.
66 - 6-6.
67 - 6-7.
68 - 6-8.
69 - 6-E.
70 - The level intro is glitched and Yoshi spawns in the sky. There does not appear to be a floor.
71 - Yoshi spawns at the top left of 1-1, similar to having done a pipe jump.
72 - The level intro is glitched and Yoshi spawns in a dark house with light around him. There does not appear to be a floor.
73 - The level intro is very glitchy and Yoshi spawns in the top left of 1-1, similar to having done a pipe jump. Yoshi's colors are an inverted type of green.
74 - The level intro is blank and Yoshi spawns below the middle-ring in 6-2.
75 - The level intro is blank and Yoshi spawns in the sky of a boss room background with Kamek music playing. There does not appear to be a floor.
76 - The level intro is blank and Yoshi spawns in the sky of a waterfall background similar to 4-2. There does not appear to be a floor. Yoshi's colors are a metallic blue.
77 - The level intro is blank and Yoshi spawns in the sky of a jungle background. There is a very short drop to death and there does not appear to be a floor. Yoshi's colors are a mix green, blue and gray and Baby Mario is purple and orange.
78 - The level intro is glitchy with no text and a small Raphael is visible. The level looks like the Raphael boss fight on the moon but incredibly glitched and sideways. A text box appears slowly and Raphael rotates slowly as well. A few random sprites come from the side of the screen and then the game softlocks.
79 - This one is similar to 77 coins except with a brown/green/blue color palette.
80 - 1-1.
81 - Yoshi is metallic blue and spawns in a locked section of 4-4. You can go back and play 4-4 like normally but Yoshi retains the wrong colors.
82 - The level intro is similar to 78 coins but the game softlocks after the level music starts to play.
83 - Yoshi is yellowish and spawns in the middle of some foam in 3-5. The foam pushes you left to your death.
84 - Yoshi is monochromatic and spawns in the sky. There does not appear to be a floor and fluttering to the right results in the screen changing.
85 - Yoshi is ketchup colored and spawns in the top left of 1-1, similar to having done a pipe jump.
86 - This one is similar to 78 coins. Raphael slowly rotates all the way around the moon, looks around and pounds the ground. You have control over Yoshi and if you flutter, the moon will rotate. This will spawn a bunch of random sprites and will likely softlock the game.
87 - This one is very similar to 86 coins except it may spawn different sprites.
88 - Yoshi is glitchy colored and spawns in the sky of a jungle background. At least one invisible platform is located at the bottom of the far right of the screen.
89 - Yoshi is yellow/green colored and spawns in the middle of 4-6. The level appears to be normal otherwise.
90 - Yoshi is glitchy colored and spawns in the sky of a snow level while the bonus music plays. There does not appear to be a floor.
91 - Yoshi is the regular light blue color and spawns in the sky of 1-1, similar to having done a pipe jump.
92 - The level intro is glitched. Yoshi is strangely colored and spawns in the "air" of an underwater background. There does not appear to be a floor.
93 - The level intro is blank. Yoshi is the regular purple color and spawns in the sky of 1-1, similar to having done a pipe jump.
94 - This one is similar to 78 coins. A glitched Bullet Bill Cannon sprite appears in place of Raphael, which wanders in a circle around the moon (or whatever it could be) forever. Yoshi spawns on top of the level and is able to move once the glitched Raphael sprite does. Going to the left causes very bright colored lines to flood the screen. Going to the right spawns a very glitched GOAL! sprite to appear. Both directions will cause a softlock. Yoshi can get hit by the glitched Raphael sprite and can also fall to his death. Upon death, the game asks if you want to restart at the middle-ring. A glitched, orange colored Yoshi then spawns on a red coin in level 1-1.
95 - Yoshi is a glitched purple color and spawns in the sky of 1-1, similar to having done a pipe jump.
96 - 1-1.
97 - Yoshi is glitched colored and spawns in the sky with a background of happy little mountains. Horizontal speed is low but vertical speed is very high. The screen appears to wrap vertically a few times. There does not appear to be a floor.
98 - The level intro is, similar to 92 coins. Yoshi is the regular light blue color and spawns in the sky.
99 - Similar to 97 coin.