Statistical mechanical systems can be described by very high-dimensional energy landscapes. These landscapes are in turn described by their stationary points (minima, saddles, & maxima). Many thermodynamic properties of the original system can be recovered from a catalogue of these stationary points. In this talk I will give some background on the energy landscape perspective of statistical systems, describe some existing theoretical work that links stationary points to thermodynamics, and tell about an energy landscape explorer I am building that numerically explores a given landscape, searching for all its stationary points.