In this review paper we investigate the connection between gravity and electromagnetism from Faraday to the present day. The particular focus is on the connection between gravitational and electromagnetic radiation. We discuss electromagnetic radiation produced when a gravitational wave passes through a magnetic field. We then discuss the interaction of electromagnetic radiation with gravitational waves via Feynman diagrams of the process graviton + graviton → photon + photon. Finally we review recent work on the vacuum production of counterpart electromagnetic radiation by gravitational waves.