The superconductor-insulator transitions of quench-condensed ultrathin films of metals are simple examples of continuous quantum phase transitions. Quantum phase transitions differ from thermal phase transitions in that they occur at zero temperature when the ground state of a system is changed in response to a variation of an external parameter of the Hamiltonian. In superconductor-insulator transitions, this control parameter is usually a parallel or perpendicular magnetic field, disorder, or charge density. Quantum phase transitions are studied through measurements, at nonzero temperature, of physical behavior influenced by the quantum fluctuations associated with the transition. Here we focus on the results of transport and magnetotransport measurements of disordered quench-condensed films of metals that are effectively two-dimensional. Open questions relating to the nature of the very puzzling insulating regime and whether there are several different types of superconductor-insulator transitions determined by material properties will be discussed.