This review addresses field-reversed configurations (FRCs), which are compact-toroidal magnetic systems with little or no toroidal field and very high β (ratio of plasma pressure to magnetic pressure). Although enthusiasm for the FRC has primarily been driven by its potential for an attractive fusion reactor, this review focuses on the physics rather than on technological or engineering aspects. Major advances in both theory and experiment have taken place since the previous comprehensive FRC review in 1988. Even so many questions remain. In particular, even though FRC experiments have exhibited remarkable stability, how well this extrapolates to larger systems remains unresolved. The review considers FRCs under familiar topical categories: equilibrium, global stability, self-organization, transport, formation, and sustainment.