  This paper is a brief journey into the amazing realm of crystalline color
superconductors. Starting from a qualitative description of superfluids,
superconductors and supersolids, we show how inhomogeneous phases may arise
when the system is under stress. These basic concepts are then extended to
quark matter, in which a richer variety of phases can be realized. Then, the
most interesting properties of the crystalline color superconductors are
presented. This brief journey ends with a discussion of crystalline color
superconductors in compact stars and related astrophysical observables. We aim
at providing a pedagogical introduction for nonexpert in the field to a few
interesting properties of crystalline color superconductors, without discussing
the methods and the technicalities. Thus, the results are presented without a
proof. However, we try to give a qualitatively clear description of the main
concepts, using standard quantum field theory and analogies with condensed
matter systems.
