Super Smash Bros. Melee and Super Smash Bros. Brawl that does just as one would expect - it gives temporary invincibility frames to the user in the air, preventing attacks from hitting them. It has sometimes been described as sidestepping in midair.
 In Super Smash Bros. Melee
In Melee, an air dodge is performed by fully pressing L or R while in the air. Air dodging cannot be done if the character is tumbling or reeling. The air dodge halts the character's momentum, either leaving him or her hovering if the Control Stick is not tilted or giving the character a small boost in the direction of the Control Stick. This boost can aid one's recovery, though most air dodging characters cannot sweet spot the ledge, and most third jumps outreach the air dodge.
During the air dodge, the character cannot be hit by attacks, but then enters a helpless state and falls to the ground.
An angled recovery is the opposite of wavedashing, since the player angles the control stick up. An angled recovery is useful when a player gets knocked off a stage that has multiple platforms, such as Temple.
In order to perform an angled recovery, a player must hold the control stick up diagonally and air dodge. The angled recovery has less lag time compared to a character's normal recovery and it can't be negated since the player invincible, but it generally doesn't go as far as a character's usual recovery move. The angled recovery is useful when the player is at the peak of their second jump from a short vertical distance off the side of the stage (usually 1.5 inches below the edge of the stage at most) and a short horizontal distance (usually .5 inches away from the stage at most). If the player is too far away, they will fall and receive a self-destruct. The player can also perform this at far distances only if they're at a very high altitude. The angled recovery is effective when the character's second jump isn't enough to make it back to the stage, but is close enough for where an air dodge will cover the remaining recovery distance. Angled recoveries are most beneficial for Jigglypuff and Yoshi, since their up B attacks do not give any recovery distance, though with Jigglypuff, its jumps and Rising Pound can usually get it back to the stage anyway. Angled recoveries are also particularly helpful to a lone Popo, who lacks a proper recovery move. Air dodging does not lead the user immediately into helplessness, so that characters that have wall-grapples can use it out of an air dodge. A similar maneuver allows to grab items while air dodging.
Characters with effective recoveries (including side special moves) such as Falco (Fire Bird and Falco Phantasm), Peach (floating and Peach Parasol), Fox (Fire Fox and Fox Illusion), Marth (Dolphin Slash and Dancing Blade), and Pikachu (Quick Attack and Skull Bash), rarely need to use the angled recovery or elevated recovery since their recoveries are tougher to block if done with proper timing.
 In Super Smash Bros. Brawl
In Brawl, the air dodge has been revamped. It no longer halts the character's momentum and no longer permits the user to nudge the character by pressing the control stick. It simply grants brief invincibility along the character's current line of movement. Following the air dodge, characters are put in their regular aerial state rather than the helpless state, and thus may attack, jump, or air dodge again following their initial air dodge.
The air dodge can now also be used when a character is tumbling or reeling, and is often employed by players to enable action quicker than waiting out their knockback and to limit reliance on teching. Using the air dodge at this time does not reduce knockback, a rumor that was started when it was noticed that higher-level CPUs were doing it constantly. However, an air dodge can be used for momentum canceling, and in some cases, such as Ike and Snake, it is their best option, since they yield better results using an air dodge when momentum canceling than their shortest lasting aerial (both of their air dodges end in 39 frames, while their shortest lasting aerials last just a few frames longer, and despite the miniscule difference, air dodging is still their best option nonetheless). In addition, they also gain the most benefit when Momentum Canceling using the basic method.
Air dodging will cause the character to automatically catch any item nearby during the first frames. This does not work if the character already has an item, though.
 Air dodge invincibility and lag in Brawl
The numbers before the / are the invincibility frames of the air dodge, and the number after the / is the total number of frames taken to perform the air dodge. For example, Meta Knight's air dodge takes 39 frames to perform, but he is only invincible between frames 3 and 29.
3-29 / 39
4-29 / 39
4-29 / 48
4-30 / 49
4-29 / 49
5-30 / 49
4-19 / 49