Axe

"Axes were first added to Minecraft in January 2010, in version 0.31. They were double-headed to begin with, then one of the heads was removed, then it was put back and the other removed to get the tool that we have today. They’ve stayed much the same over the years – with the biggest changes in the combat update, tweaking damage and attack speed."

- Duncan Geere

An axe is a tool used to hasten the collection of wood-based items. It is also used as a weapon for melee attacks. In the most recent update, axes are labeled as doing 9 damage, but they actually don't.

Unit repair
An axe can be repaired in an anvil by adding units of the tiers' repair material, with each repair material restoring 25% of the axe's maximum durability, rounded down.

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

Raids
In Bedrock Edition vindicators and pillagers that spawn in raids have a 4.1% chance (5.12% on hard) to drop a badly-damaged iron axe, which is sometimes enchanted with a random enchantment. It is possible for a vindicator 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 always offer to sell an enchanted diamond axe for 18-35 emeralds.

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

Durability
Each tier of axe has a different durability:

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

Stripped logs/wood
an axe on a log or wood block causes it to become a stripped log or a stripped wood block, respectively. This consumes one point of 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.

The difference between the two is that a sword does a swipe attack, spreading a splash damage to multiple nearby entities, while an axe concentrates its damage on a single target. An axe loses 2 points of durability when used as a weapon. The damage dealt and cooldown time depends 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. Mobs armed with axes (vindicators or others with commands) always disable the player's shield.

Bedrock Edition
$$, 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.