Efficient computational tools allow us to catalogue the stationary points and topographies of systems of as many as 12-15 particles, but to interpret larger systems, we must use statistical methods.  Databases whose elements are sequences of adjacent minima, connected by the saddle points between them, provide the information to carry out such interpretations. Generalizations that emerge are these: sawtooth-like topographies appear to be associated with short-range potentials, with few-particle motions from one minimum to the next and with easy formation of amorphous structures, while staircase-like potentials arise from long-range interactions, highly collective well-to-well motions and strong structure-seeking character, whether crystallizing or folding. The information about the sequences of stationary points allows us to construct master equations for the time
evolution of arbitrary distributions on the surface and to determine optimal temperature programs to approach target distributions of particle energies and morphologies.