Axe

Axes are tools used to ease the process of collecting wood-based items and for melee attack.

Unit repair
An axe can be repaired in an anvil by adding units of the corresponding material, each restores 25% its maximum durability, rounded down.

Equipment
A vindicator spawns with an iron axe, and has an 8.5% (9.5% with Looting I, 10.5% with Looting II and 11.5% with Looting III) chance of dropping it upon death by the player. It will usually have some level of damage, and will sometimes be enchanted.

Raid
In Bedrock Edition vindicators and pillagers that spawn in raids have a 4.1% chance (5.12% on hard) to drop an iron axe, which will be badly damaged and sometimes enchanted with a random enchantment. It's possible for vindicators to drop 2 iron axes, one from natural equipment and one from raid drops.

Trading
Novice-level Toolsmith villagers have a 25% chance to sell a stone axe for one emerald, journeyman-level Toolsmith villagers have a 25% chance to sell an enchanted iron axe for one emerald, and expert-level Toolsmith villagers have a 50% chance to sell an enchanted diamond axe for 12 emeralds.

Novice-level Toolsmith villagers have a 40% chance to sell a stone axe for one emerald, journeyman-level Toolsmith villagers have a 40% chance to sell an enchanted iron axe for 7-22 emeralds, and expert-level Toolsmith villagers have a $2/3$ chance to sell an enchanted diamond axe for 18-35 emeralds.

Novice-level Weaponsmith villagers sell an iron axe for 3 emeralds as one of their trades and master-level Weaponsmith villagers sell an enchanted diamond axe for 12 emeralds.

Novice-level Weaponsmith villagers have a $2/3$ chance to sell an iron axe for 3 emeralds. Master-level Weaponsmith villagers will always sell an enchanted diamond axe for 18-35 emeralds.

The enchantments will be the same as the ones obtained from an enchantment table at levels 5–19.

Natural generation
In woodland mansions, a sealed room can appear that has a chest always containing an Efficiency I iron axe.

Chopping wood
An ахе is used to break logs and blocks derived from it faster than by using other tools. An axe uses 1 durability to break a block. For blocks that break instantly, it uses 0 durability.

Speed and durability
The following table summarizes the speed at which axes of different qualities perform.

Stripped logs/wood
an axe on a log or wood block will cause it to become a stripped log or a stripped wood block, respectively. This will consume one durability from the axe.

Java Edition
Damage done when using an axe as a weapon is more than that of a sword, though they take longer than a sword to recover. Axes lose 2 points of durability when used as a weapon, and deal different amount of damage and have different cooldown times based on the type:

Disabling shields
Attacking a shield user with an axe has a chance to disable the use of the shield for 5 seconds. The base chance is 25%, plus 5 percentage points per level of Efficiency on the axe, plus 75 percentage points if attacking while sprinting.

Bedrock editions
$$, axes always attack instantly (without a cooldown) and do less damage than a sword of the same quality:

Enchantments
An axe can receive the following enchantments:

Fuel
Wooden axes can be used as a fuel in furnaces, smelting 1 item per axe.

Video
Note: This video is outdated, since as of 15w34c axes actually deal more damage than a sword.

Trivia

 * Before Java Edition 1.13, in the language files, axes were referred to as Hatchets.