  Time crystals are physical systems whose time translation symmetry is
spontaneously broken. Although the spontaneous breaking of continuous
time-translation symmetry in static systems is proved impossible for the
equilibrium state, the discrete time-translation symmetry in periodically
driven (Floquet) systems is allowed to be spontaneously broken, resulting in
the so-called Floquet or discrete time crystals. While most works so far
searching for time crystals focus on the symmetry breaking process and the
possible stabilising mechanisms, the many-body physics from the interplay of
symmetry-broken states, which we call the condensed matter physics in time
crystals, is not fully explored yet. This review aims to summarise the very
preliminary results in this new research field with an analogous structure of
condensed matter theory in solids. The whole theory is built on a hidden
symmetry in time crystals, i.e., the phase space lattice symmetry, which allows
us to develop the band theory, topology and strongly correlated models in phase
space lattice. In the end, we outline the possible topics and directions for
the future research.
