The Fermi Large Area Telescope has dramatically expanded the sample of gamma-ray pulsars and discovered the new population of gamma-ray emitting millisecond pulsars. The quality of pulsar light curves and spectra is exceptional, and allows a direct study of the magnetospheric processes that lead to the emission of gamma-rays. I will review the theoretical understanding (and misunderstanding) of pulsar magnetospheres and discuss how gamma-ray light curves and spectra can be used to determine the location of the emitting zones and the geometry of the magnetic field. It is now clear that the emission is coming from the outer magnetosphere, where the deviations from dipolar field geometry due to plasma currents must be taken into account. I will compare the modeling of light curves using both vacuum and plasma-filled (force-free) magnetic geometries. The accelerating regions, which have to be postulated in the vacuum model, seem to be related to the location of strong currents in plasma-filled magnetosphere. Plasma physics and particle acceleration in these current sheets needs to be understood, and it will be strongly constrained by modeling of the phase-resolved spectra from Fermi. Gamma rays carry a significant fraction of spin down energy in pulsars, thus Fermi observations are already probing the heart of the electromagnetic pulsar machine.