Coral

Coral (coral plant) is a block that can only be placed underwater. It comes in five variants: tube, brain, bubble, fire, and horn.

Coral block (coral) is a solid block which comes in the same variants as corals.

Dead coral block (dead coral) is a solid block which also comes in the same variants as corals.

Coral fans are blocks that can only be placed underwater, on the 4 sides of blocks: north, south, west, east. Like coral, they come in five variants, and they have a dead variant in Bedrock Edition.

Obtaining
Coral blocks and dead coral blocks will only drop as an item if mined with any type of pickaxe. Otherwise, they will drop nothing.

Coral plants and fans can be instantly mined and will always drop themselves.

Natural generation
Coral, coral blocks, and coral fans naturally generate in coral reef structures. These are found in warm oceans.

In the Java Edition, coral fans do not generate naturally.

Usage
All 4 types and variants of coral can be used as a building or decoration block.

Dead coral blocks
In order for coral blocks to stay alive, at least 1 of the blocks touching it must be water. If it's placed outside of water, it will instantly and irreversibly transform into its respective dead coral block.

Trivia

 * Despite being called plants in the game, in real life corals are actually colonies of sessile (immobile) animals.