The deepest cave in the world found up to 1992 is in France, the Reseau Jean Bernard.
Its total depth, not just the length of its shaft, is 5,256 feet, almost a mile straight down.
The longest system of underground passageways in the world is the Mammoth Cave system in Kentucky.
The numbers change with new exploration, but as of June 1991, the sum of all known passages was 340 miles.
The deepest cave known in the United States is a new discovery, Lechuguilla Cave, in Carlsbad Caverns National Park, New Mexico.
Its depth is 1,565 feet.
A large part of the United States is underlain by cavernous limestone aquifers.
The Mammoth Cave National Park system was basically formed by the solution of limestone. As water falls on the surface of the earth, it mixes with organic matter and forms a weak solution of carbonic acid, like weak Coca-Cola.
Given sufficient time, perhaps millions of years, the solution feeds into the cavities of the limestone and gradually creates a cave, a little like tooth decay.
Amateur exploration of caves is an important source of knowledge about them and can be safe if undertaken by properly trained and supervised people.
For example, from the standpoint of structural stability, caves are relatively much safer than mines.