Some 2D quantum many-body systems with a bulk energy gap support gapless edge modes which are extremely robust. These modes cannot be gapped out or localized by general classes of interactions or disorder at the edge: they are "protected" by the structure of the bulk phase. Examples of this phenomena include quantum Hall states and 2D topological insulators, among others. Recently, much progress has been made in understanding protected edge modes in non-interacting fermion systems. However, less is known about the interacting case. A basic problem is to predict, for general interacting systems, when such edge modes are present or absent, and to identify the different physical mechanisms that underlie their stability. In this talk, I will discuss this problem in the simplest case: interacting fermion systems without any symmetry.