The Large Area Telescope (LAT) on the Fermi satellite is the first gamma-ray instrument to discover pulsars directly via their gamma-ray emission. Roughly one third of the 117 gamma-ray pulsars detected by the LAT in its first three years were discovered in blind searches of gamma-ray data and most of these are undetectable with current radio telescopes. I review some of the key LAT results and highlight the specific challenges faced in gamma-ray (compared to radio) searches, most of which stem from the long, sparse data sets and the broad, energy-dependent point-spread function (PSF) of the LAT. I discuss some ongoing LAT searches for gamma-ray millisecond pulsars (MSPs) and gamma-ray pulsars around the Galactic Center. Finally, I outline the prospects for future gamma-ray pulsar discoveries as the LAT enters its extended mission phase, including advantages of a possible modification of the LAT observing profile.