Multidimensional potential energy surfaces for systems larger than about 15 atoms are so complex that interpreting their topographies and the consequent dynamics requires statistical analyses of their minima and saddles. Sequences of minimum-saddle-minimum points provide a characterization of such surfaces. Two examples, Ar ₁₉ and (KCI) ₃₂ , illustrate how topographies govern tendencies to form glasses or “focused” structures, for example, crystals or folded proteins. Master equations relate topographies to dynamics. The balance between glass-forming and structure-seeking characters of a potential energy surface seems governed by sawtooth versus staircase topography and the associated collectivity of the growth process after nucleation.