Our current understanding of the physical processes of star formation is reviewed, with emphasis on processes occurring in molecular clouds like those observed nearby. The dense cores of these clouds are predicted to undergo gravitational collapse characterized by the runaway growth of a central density peak that evolves towards a singularity. As long as collapse can occur, rotation and magnetic fields do not change this qualitative behaviour. The result is that a very small embryonic star or protostar forms and grows by accretion at a rate that is initially high but declines with time as the surrounding envelope is depleted. Rotation causes some of the remaining matter to form a disk around the protostar, but accretion from protostellar disks is not well understood and may be variable. Most, and possibly all, stars form in binary or multiple systems in which gravitational interactions can play a role in redistributing angular momentum and driving episodes of disk accretion. Variable accretion may account for some peculiarities of young stars such as flareups and jet production, and protostellar interactions in forming systems of stars will also have important implications for planet formation. The most massive stars form in the densest environments by processes that are not yet well understood but may include violent interactions and mergers. The formation of the most massive stars may have similarities to the formation and growth of massive black holes in very dense environments.