Discrete approaches to gravity, both classical and quantum, are reviewed briefly, with emphasis on the method using piecewise-linear spaces. Models of three-dimensional quantum gravity involving 6j-symbols are then described, and progress in generalizing these models to four dimensions is discussed, as is the relationship of these models in both three and four dimensions to topological theories. Finally, the repercussions of the generalizations are explored for the original formulation of discrete gravity using edge-length variables.