  The idea of a Potential Energy Surface (PES) forms the basis of almost all
accounts of the mechanisms of chemical reactions, and much of theoretical
molecular spectroscopy. It is assumed that, in principle, the PES can be
calculated by means of clamped-nuclei electronic structure calculations based
upon the Schr\"{o}dinger Coulomb Hamiltonian. This article is devoted to a
discussion of the origin of the idea, its development in the context of the Old
Quantum Theory, and its present status in the quantum mechanics of molecules.
It is argued that its present status must be regarded as uncertain.
