Supersonic jets, particularly shock-containing jets, often exhibit high-intensity, discrete-frequency acoustic tones. These tones are the signature of an aeroacoustic resonance loop established by the flow. This paper considers two of the classical forms of supersonic jet resonance: screech in shock-containing free jets and tones generated by the impingement of a jet against a surface. The first half of the paper provides a historical perspective on research into both forms of resonance, ranging from the seminal works of Alan Powell to recent contributions from high-fidelity numerical simulation, experiment, and stability theory. The second half of the paper provides a critical assessment of current understanding around the four processes that characterize jet resonance: a downstream propagation of energy, an acoustic generation mechanism, an upstream propagation of energy, and a receptivity mechanism.