Pease and Shapley (1917) first remarked on the apparent flattening of several Galactic globular clusters, a view that has been confirmed by many subsequent studies. Tidal stresses, internal rotation, and velocity anisotropies can cause deviations from sphericity in stellar systems. In general, we might expect globular clusters to have some angular momentum at the time of formation and, if they collapsed from flattened initial conditions, to have anisotropic pressure support. Since the velocity distributions within the clusters can be altered by a variety of internal and external processes, their shapes are expected to evolve. In this article, we review the methods for measuring ellipticities and the results that have emerged from such studies. Our main purpose, however, is to discuss the processes that determine the shapes of globular clusters and the ways in which they change with time.