The general circulation of the ocean plays a major role in the global climate system, and the local circulation in near-shore regions is also of substantial scientific and societal interest. This talk will give an introduction to some of the physical and computational issues that arise when ocean circulation is modeled numerically. These include motivations for ocean modeling; length, time, and mixing scales; the choice of vertical coordinate; governing equations; multiple time scales and time-stepping; spatial grids and discretization schemes; and some current work and upcoming issues.