What are cats' tails for?

What are cats' tails for? Two uses come to mind immediately.  Cats' tails are used for balance. In the domestic cat this use is somewhat redundant. For wildcats it is very much alive. Many wild cats are tree dwelling such as the margay and clouded leopard. These cats have long tails. Tails that are used for balance are also frequently very thick. I am thinking of the snow leopard that lives on 40 degree rocky inclines where excellent balance is paramount.

Although the domestic cat does not need the tail for balance as much it has developed another use of the tail, a form of visual communication through body language.

The wagging tail means that the cat is in mental conflict (out of balance mentally and not physically). This happens when he or she is uncertain about what to do.

The domestic and feral cat also uses the tail in the upright position to signal a friendly greeting. The tail position is used as a form of body language.

Cats that have bob tails or shortened tails are at a slight disadvantage. The bobcat comes to mind for the wild cats and the Japanese Bobtail is one example of a purebred cat without a normal length tail.

The bobcat is a ground hunter and probably does not need its tail for balance when chasing prey as much as the cheetah which is a much faster cat (max 64 mph compared to about 40+ at a guess for the bobcat).