Magnetic multilayers which incorporate ultrathin ferromagnetic films are physical realizations of classical, one dimensional spin systems, with spins coupled via exchange mediated by spacer layers or interactions at interfaces, and subject to anisotropy. Here by `spin', we refer to the total spin angular momentum of an ultrathin film in the structure. Such systems can undergo a rich range of phase transitions, in reponse to an external magnetic field, or change in temperature. Since interfilm exchange is weak, modest magnetic fields can induce spin reorientation phase transitions. We thus have a new and diverse class of magnetic materials, with phase diagrams subject to design, since both thickness, composition, or growth conditions. The paper reviews selected examples, including recent studies of the dynamic response (AC susceptibility) of an antiferromagnetically coupled Fe/Cr system which undergoes the surface spin-flop transition.