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Caverns are reservoirs of liquid (water, lava, or acid) found underground in the Overworld and in the Nether.
Caverns are randomly generated underground in the Overworld. They consist of a pool of liquid and an air pocket above it. The depths of both of these are randomly generated, and are different for each column in the cavern. The liquid found in the pool can be any naturally generating liquid, either water, lava, or acid, and this is the same throughout the cavern. There are sometimes random blocks of stone or ores in the air pockets above the liquid.
In the Nether, caverns generate in a similar way, however instead of stone they have netherrack, and they can only generate with lava.
A water cavern in 1.4.34. This was before caverns were randomly generated, and always had this structure.