ABSTRACT:  Cellular structures are compact domains joined along codimension 1 interfaces to fill space.  Such cellular microstructures are ubiquitous in materials science and biology.  I will briefly review the basic theory of cellular structure evolution via capillarity (surface tension) forces and then discuss some recent simulation results for such evolving microstructures.  The main focus of the presentation will be on the analysis of the structure of these cellular ensembles - including both geometric and topological measures.