A general theory of mesh-refinement processes is developed. The fundamental structure is a locally finite, rooted tree with nodes representing the subdivision cells. The possible meshes then constitute a distributive lattice. Under mild conditions on the given cell-size and error-indicator functions a local Pareto-type optimality property is introduced for the meshes. This in turn is used to prove some general rate-of-convergence and global optimality properties which contain various known results of this type for specific problems.