  Materials with thickness ranging from a few nanometers to a single atomic
layer present unprecedented opportunities to investigate new phases of matter
constrained to the two-dimensional plane.Particle-particle Coulomb interaction
is dramatically affected and shaped by the dimensionality reduction, driving
well-established solid state theoretical approaches to their limit of
applicability. Methodological developments in theoretical modelling and
computational algorithms, in close interaction with experiments, led to the
discovery of the extraordinary properties of two-dimensional materials, such as
high carrier mobility, Dirac cone dispersion and bright exciton luminescence,
and inspired new device design paradigms. This review aims to describe the
computational techniques used to simulate and predict the optical, electronic
and mechanical properties of two-dimensional materials, and to interpret
experimental observations. In particular, we discuss in detail the particular
challenges arising in the simulation of two-dimensional constrained fermions,
and we offer our perspective on the future directions in this field.
