Recent experimental advances in the field of cavity quantum electrodynamics (QED) have opened new possibilities for control of atom-photon interactions. A laser with "one and the same atom" demonstrates the theory of laser operation pressed to its conceptual limit. The generation of single photons on demand and the realization of cavity QED with well defined atomic numbers N = 0, 1, 2,... both represent important steps toward realizing diverse protocols in quantum information science. Coherent manipulation of the atomic state via Raman transitions provides a new tool in cavity QED for in situ monitoring and control of the atom-cavity system. All of these achievements share a common point of departure: the regime of strong coupling. It is thus interesting to consider briefly the history of the strong coupling criterion in cavity QED and to trace out the path that research has taken in the pursuit of this goal.