  Inducing long-range magnetic order in three-dimensional topological
insulators can gap the Diraclike metallic surface states, leading to exotic new
phases such as the quantum anomalous Hall effect or the axion insulator state.
These magnetic topological phases can host robust, dissipationless charge and
spin currents or unique magnetoelectric behavior, which can be exploited in
low-energy electronics and spintronics applications. Although several different
strategies have been successfully implemented to realize these states, to date
these phenomena have been confined to temperatures below a few Kelvin. In this
review, we focus on one strategy, inducing magnetic order in topological
insulators by proximity of magnetic materials, which has the capability for
room temperature operation, unlocking the potential of magnetic topological
phases for applications. We discuss the unique advantages of this strategy, the
important physical mechanisms facilitating magnetic proximity effect, and the
recent progress to achieve, understand, and harness proximity-coupled magnetic
order in topological insulators. We also highlight some emerging new phenomena
and applications enabled by proximity coupling of magnetism and topological
materials, such as skyrmions and the topological Hall effect, and we conclude
with an outlook on remaining challenges and opportunities in the field.
