We describe a multiresolution representation for meshes based on subdivision. Subdivision is a natural extension of the existing patch-based surface representations. Subdivision algorithms can also be viewed as operating directly on polygonal meshes, which makes them a useful tool for mesh manipulation. Combining subdivision and the smoothing algorithms of Taubin~\cite{Taubin:1995:SPA} allows us to construct a set of algorithms for interactive multiresolution editing of complex meshes of arbitrary topology. The simplicity of the underlying algorithms for refinement and coarsification, enables us to make them local and adaptive, considerably improving their efficiency. We have built a scalable interactive multiresolution editing system based on such algorithms.