In 2005 researchers demonstrated for the first time the ability to allow punctures to move through the coordinate system, thus eliminating some of the earlier problems with the method. This allowed accurate long-term evolutions of black holes. By choosing appropriate coordinate conditions and making crude analytic assumption about the fields near the singularity (since no physical effects can propagate out of the black hole, the crudeness of the approximations does not matter), numerical solutions could be obtained to the problem of two black holes orbiting each other, as well as accurate computation of gravitational radiation (ripples in spacetime) emitted by them.