FINUFFT is a library to compute efficiently three types of nonuniform fast Fourier transform (NUFFT), to a specified precision, in one, two, or three dimensions, The library has a very simple interface, has a multithreaded CPU version (C++/OpenMP) and a GPU version (CUDA). It has detailed documentation, tutorials, and wrappers to C, Fortran, MATLAB, Octave, Python, and Julia.