The dynamics of interacting populations are often modeled using differential (or difference) equations on the non-negative cone of Euclidean space. A fundamental question about these dynamics is "what are the minimum conditions to ensure the long-term persistence of the populations?" One definition of persistence widely used in the ecological and mathematical literature is permanence that corresponds to the existence of a positive global attractor. In addition to allowing a diversity of dynamical behaviors, permanence has the advantage that it can be verified with a variety of mathematical techniques. In this talk, I will discuss some of these techniques and their application to several models. Of particular interest are models that admit heteroclinic cycles between invariant sets of the boundary of the non-negative cone. These heteroclinic cycles typically correspond to intransitivities in the ecological dynamics (e.g. community A displaces community B, community B displaces community C, and community C displaces community A) and arise naturally in higher dimensional models. I will discuss how these heteroclinic cycles yield an open set of ecological models for which persistence remains undecided. Namely, within this open set there is a dense subset of permanent models and another dense subset of models that admit an attractor on the boundary.