mpi4py-fft is a Python package for computing Fast Fourier Transforms (FFTs). Large arrays are distributed and communications are handled under the hood by MPI for Python (mpi4py). To distribute large arrays we are using a new and completely generic algorithm that allows for any index set of a multidimensional array to be distributed. We can distribute just one index (a slab decomposition), two index sets (pencil decomposition) or even more for higher-dimensional arrays. mpi4py-fft comes with its own Python interface to the serial FFTW library. This interface can be used much like pyfftw, and even for real-to-real transforms, like discrete cosine or sine transforms.