Recently, some new surprisingly-elegant stable periodic solutions to the 4-body problem were discovered.  I will review the current state-of-the-art for finding periodic solutions to the n-body problem and I will describethe interesting new ones that have been found.  I will also discuss the key question of the stability of these orbits.  Some are unstable (hence uninteresting), some are quasi-stable (meaning that they exhibit a ``locally'' chaotic behavior but don't blow up), while a few are amazingly stable.