There are no practical limits to the precision except the ones implied by the available memory in the machine GMP runs on (operand dimension limit is 2^(32)-1 bits on 32-bit machines and 2^37 bits on 64-bit machines).
GMP has a rich set of functions, and the functions have a regular interface. The basic interface is for C but wrappers exist for other languages including Ada, C++, C#, OCaml, Perl, PHP, and Python.