The influence of surface orography on patterns of precipitation gives rise to some of the most pronounced climate gradients on Earth, and plays a fundamental role in the interaction between the atmosphere and the rest of the Earth System on a wide variety of time scales. The physical mechanisms involved comprise a rich set of interactions encompassing fluid dynamics, thermodynamics, and micron-scale cloud processes, as well as being dependent on the larger-scale patterns of the atmospheric general circulation. Investigations into orographic precipitation have pursued three parallel tracks of inquiry: observations, theory, and modeling. Significant advances have been made in each over the last few decades, and these are summarized and synthesized here. While many aspects of the basic mechanisms responsible for orographic precipitation have been understood, important issues remain unresolved. The sheer number of contributing processes, together with their convoluted interactions, make the quantitative prediction of precipitation in complex terrain a very hard task. However, while prediction of precipitation amounts for any given event may be difficult, various lines of evidence suggest that the patterns of orgraphic precipitation, even on scales of a few kilometers, are much more robust.