K3Match is a C library with Python bindings for fast matching of points in 3D space. It uses an implementation of three dimensional binary trees to efficiently find matches between points in 3D space. Two lists of points are compared and match indices as well as distances are given. K3Match can find either the nearest neighbour or all matches within a given search distance in 3D Cartesian space or on the surface of the 2D unit sphere in standard spherical or celestial coordinates.