  One of the intriguing properties characteristic to three-dimensional
topological materials is the topological magnetoelectric phenomena arising from
a topological term called the $\theta$ term. Such magnetoelectric phenomena are
often termed the axion electrodynamics, since the $\theta$ term has exactly the
same form as the action describing the coupling between a hypothetical
elementary particle, axion, and a photon. The axion was proposed about forty
years ago to solve the so-called strong CP problem in quantum chromodynamics,
and is now considered as a candidate for dark matter. In this tutorial, we
overview theoretical and experimental studies on the axion electrodynamics in
three-dimensional topological materials. Starting from the topological
magnetoelectric effect in three-dimensional time-reversal invariant topological
insulators, we describe the basic properties of static and dynamical axion
insulators whose realizations require magnetic orderings. We also discuss the
electromagnetic responses of Weyl semimetals with a focus on the chiral
anomaly. We extend the concept of the axion electrodynamics in condensed matter
to topological superconductors, whose responses to external fields can be
described by a gravitational topological term analogous to the $\theta$ term.
