  We discuss recent advances in the study of topological insulators protected
by spatial symmetries by reviewing three representative, theoretical examples.
In three dimensions, these states of matter are generally characterized by the
presence of gapless boundary states at surfaces that respect the protecting
spatial symmetry. We discuss the appearance of these topological states both in
crystals with negligible spin-orbit coupling and a fourfold rotational
symmetry, as well as in mirror-symmetric crystals with sizable spin-orbit
interaction characterized by the so-called mirror Chern number. Finally, we
also discuss similar topological crystalline states in one-dimensional
insulators, such as nanowires or atomic chains, with mirror symmetry. There,
the prime physical consequence of the non-trivial topology is the presence of
quantized end charges.
