We present a summary of the Fermi Pulsar Search Consortium (PSC), an international collaboration of radio astronomers and members of the Large Area Telescope (LAT) collaboration, whose goal is to organize radio follow-up observations of Fermi pulsars and pulsar candidates among the LAT gamma-ray source population. The PSC includes pulsar observers with expertise using the worlds largest radio telescopes that together cover the full sky. We have performed very deep observations of all 35 pulsars discovered in blind frequency searches of the LAT data, resulting in the discovery of radio pulsations from four of them. We have also searched over 300 LAT gamma-ray sources that do not have strong associations with known gamma-ray emitting source classes and have pulsar-like spectra and variability characteristics. These searches have led to the discovery of a total of 43 new radio millisecond pulsars (MSPs) and four normal pulsars. These discoveries greatly increase the known population of MSPs in the Galactic disk, more than double the known population of so-called `black widow pulsars, and contain many promising candidates for inclusion in pulsar timing arrays.