Motivated by talks from the first day of this workshop, we discuss in more detail modelling data by multiple subspaces, a.k.a., subspace clustering. We emphasize various theoretical results supporting the performance of some of these algorithms. In particular, we study in depth the minimizer obtained by a common energy minimization and its robustness to noise and outliers. We relate this work to recent works on robust PCA. We demonstrate how such theoretical insights guide us in practical choices and discuss some important practical questions raised in early talks of this workshop: choosing optimal local neighborhoods, modeling with missing data or high corruption and practical applications. This is based on joint works with Arthur Szlam, Yi Wang and Teng Zhang.