  Topological insulators (TIs) in three space dimensions can be characterized
by a quantized magnetoelectric coefficient. However, this coupling does not
have experimentally observable consequences in the presence of time-reversal
symmetry, because the contributions of both bulk and surface states cancel each
other. Instead, the characteristic response of a TI is a nonlinear
magnetoelectric effect. Field theoretic aspects of the nonlinear
magnetoelectric response and numerical calculations for experimentally relevant
geometries are discussed. Distinct from this effect, the magnetoelectric
coupling would bind a charge $\pm e/2$ in response to a monopole, which is
referred to as Witten effect. If time reversal is broken explicitly, for
instance, by a Zeeman field acting on the surface layer, the electromagnetic
response of a TI can be described by a half-integer quantum Hall effect of
surface electrons.
