  We review the application of discrete time crystals created in a
Bose-Einstein condensate (BEC) of ultracold atoms bouncing resonantly on an
oscillating mirror to the investigation of condensed matter phenomena in the
time dimension. Such a bouncing BEC system can exhibit dramatic breaking of
time-translation symmetry, allowing the creation of discrete time crystals
having up to about 100 temporal lattice sites and suitable for hosting a broad
range of temporal condensed matter phenomena. We first consider single-particle
condensed matter phenomena in the time dimension which include Anderson
localization due to temporal disorder, topological time crystals, and
quasi-crystal structures in time. We then discuss many-body temporal condensed
matter phenomena including Mott insulator phases in time, many-body
localization in time, many-body topological time crystals and time crystals
having long-range exotic interactions. We also discuss the construction of two
(or three) dimensional time lattices, involving the bouncing of a BEC between
two (or three) orthogonal oscillating mirrors and between two oscillating
mirrors oriented at 45-degrees. The latter configuration supports a versatile
M\"obius strip geometry which can host a variety of two-dimensional time
lattices including a honeycomb time lattice and a Lieb square time lattice.
Finally, we discuss the construction of a six-dimensional time-space lattice
which is based on periodically driven BECs trapped in a three-dimensional
optical lattice.
