This article offers a general introduction to those aspects of bathymetric mapping and satellite altimetry that are relevant to bathymetry from space. We begin with a review of some of the strengths and weaknesses of conventional bathymetric measurement and mapping. This context highlights the case for and value of space-based mapping: it is the only way to achieve globally uniform resolution within reasonable time and cost. However, a space mission cannot “see” the ocean floor directly; instead, it observes gravity anomalies that can be correlated with ocean floor topography. Geological factors and physical laws limit the resolution of this technique to a particular range of spatial scales (~100 km to ~5 km). While this is not perfect, it yields an enormous improvement in the resolution of global bottom roughness over traditional methods (Figure 1).