Clustering is one of the most commonly used data exploration tools, but data often hold interesting geometric structure for which generic clustering objectives are too coarse. Subspace clustering is a simple generalization that tries to fit each cluster with a low-dimensional subspace (ie, each cluster has a low-dimensional covariance structure). This is a very useful model for many problems in computer vision and computer network topology inference. Our group has developed state-of-the-art approaches for subspace clustering when the data matrix is incomplete and in the active clustering context.