Libsharp is a collection of algorithms for efficient conversion between maps on the sphere and their spherical harmonic coefficients. It supports a wide range of pixelisations (including HEALPix, GLESP, and ECP). This library is a successor of libpsht (ascl:1010.020); it adds MPI support for distributed memory systems and SHTs of fields with arbitrary spin, and also supports new developments in CPU instruction sets like the Advanced Vector Extensions (AVX) or fused multiply-accumulate (FMA) instructions. libsharp is written in portable C99; it provides an interface accessible to other programming languages such as C++, Fortran, and Python.