Many modern materials feature a “Planckian metal”: a phase of electronic quantum matter without quasiparticle excitations, and relaxation in a time of order Planck's constant divided by the absolute temperature. The semiclassical theory of black holes predicts thermodynamic properties which are difficult to connect to a unitary quantum theory with a discrete spectrum. I will review recent progress in understanding these problems in very different fields of physics by using insights from the Sachdev-Ye-Kitaev model of many-particle quantum dynamics.