  Among a huge variety of known two-dimensional materials, some of them have
anisotropic crystal structures; examples include so different systems as a
few-layer black phoshphorus (phosphorene), beryllium nitride BeN$_4$, van der
Waals magnet CrSBr, rhenium dichalgogenides ReX$_2$. As a consequence, their
optical and electronic properties turn out to be highly anisotropic as well. In
some cases, the anisotropy results not just in a smooth renormalization of
observable properties in comparison with the isotropic case but in the
appearance of dramatically new physics. The examples are hyperbolic plasmons
and excitons, strongly anisotropic ordering of adatoms at the surface of
two-dimensional or van der Waals materials, essential change of transport and
superconducting properties. Here, we present a systematic review of electronic
structure, transport and optical properties of several representative groups of
anisotropic two-dimensional materials including semiconductors, anisotropic
Dirac and semi-Dirac materials, as well as superconductors.
