In this talk I discuss certain insights obtained from examining a number of simulation and shape analysis problems from a more geometric point of view. The presentation will cover four vignettes dealing with multiresolution simulation, shape interpolation, symmetry detection, and shape matching. The methods apply more generally to understanding the global structure of spaces of shapes and motions, suggesting that a goal for SimBios should be not only to help biologists generate simulation data but also to provide tools for understanding that data.