Abstract: It is well known that the analysis of complex energy landscapes poses problems that are both challenging and relevant. Many analytical results study global energy minimizers, convergence under a smallness assumption on the initial data, and deterministic models. Many important applied problems, on the other hand, probe different regimes and phenomena. We survey some recent examples that focus on less traditional problems such as estimating the size of energy barriers, deriving sharp relaxation rates for general initial conditions, and bounding the probability of rare events.