Since the discovery in 1993 of the figure-8 orbit by Cris Moore, a large number of periodic orbits for equal n masses have been found having beautiful symmetries and topologies. Most of these orbits are either planar or have been obtained from perturbation of planar orbits.

Recently Moore and I have found also a number of new three-dimensional periodic orbits of this kind which have cubic symmetries. We found these orbits by symmetry considerations, and by minimizing numerically the action integral directly as a function of the Fourier coefficients for the periodic orbit coordinates. I will review some of the early history of periodic orbits, discuss our method, and present video animations of recent results.