Black widows and redbacks are binary systems consisting of a millisecond pulsar in a close binary with a companion having matter driven off of its surface by the pulsar wind. X-rays due to an intrabinary shock have been observed from many of these systems, as well as orbital variations in the optical emission from the companion due to heating and tidal distortion. We have been systematically studying these systems in radio, optical and X-rays. Here we will present an overview of X-ray and optical studies of these systems, including new XMM-Newton and NuStar data obtained from several of them, along with new optical photometry.