  This tutorial review presents an overview of the basic theoretical aspects of
two-dimensional (2D) crystals. We revise essential aspects of graphene and the
new families of semiconducting 2D materials, like transition metal
dichalcogenides or black phosphorus. Minimal theoretical models for various
materials are presented. Some of the exciting new possibilities offered by 2D
crystals are discussed, such as manipulation and control of quantum degrees of
freedom (spin and pseudospin), confinement of excitons, control of the
electronic and optical properties with strain engineering, or unconventional
superconducting phases.
