metric algebraic geometry is a term proposed for the study of properties of real algebraic varieties that depend on a distance metric. the distance metric can be the euclidean metric in the ambient space or a metric intrinsic to the variety. in this talk, we introduce metric algebraic geometry through a discussion of voronoi cells, bottlenecks, offset hypersurfaces, and the reach of an algebraic variety. we also show applications to the computational study of the geometry of data with nonlinear models.