We investigate the physical mechanisms that shape the luminosity function. Beginning with the mass function of dark matter halos, we show how gas cooling, photoionization, feedback, merging and thermal conduction affect the shape of the luminosity function. We consider three processes whereby supernovae can affect the forming galaxy: (1) reheating of disk gas to the halo temperature; (2) expansion of the diffuse halo gas; (3) expulsion of cold disk gas from the halo. While feedback of form (1) is able to flatten the faint end of the luminosity function, this alone does not produce the sharp cut-off observed at large luminosities. Feedback of form (2) is also unable to solve this problem. The relative paucity of very bright galaxies can only be explained if cooling in massive halos is strongly suppressed. Conduction is a promising mechanism, but an uncomfortably high efficiency is required to suppress cooling to the desired level. If, instead, superwinds are responsible for the lack of bright galaxies, then the total energy budget required to obtain a good match to the galaxy luminosity function greatly exceeds the energy available from supernova explosions. The mechanism is only viable if the formation of central supermassive black holes play a crucial role in limiting the amount of stars that form in the host galaxy. (abridged)