We discuss efficient numerical algorithms for solving parameterized partial differential equations. These include reduced-basis methods, in which parameterized approximate solutions are constructed from a space of dimension significantly smaller than the dimension of the spatial discretization; stochastic Galerkin methods, in which a large deterministic solution is specified to produce approximate solutions that are easily evaluated; and stochastic collocation methods, in which approximation based on interpolation using so-called sparse grid methods.  We outline the properties and costs of these methods and compare their performance on benchmark problems.