Consider data points drawn from a union of subspaces (i.e., each point is drawn from one of several subspaces) with noise added. Given only these data points, the goal of subspace clustering is to cluster the points by the subspace to which they belong and to estimate the corresponding subspaces. There has been great progress in recent years on a variety of techniques for tackling this problem, but to the best of my knowledge, a method-of-moments approach has not yet been studied. Inspired by recent work on efficient symmetric tensor methods for estimating Gaussian Mixture Models, this talk will discuss work on developing a method-of-moments technique for subspace clustering.