  We review a few representative examples of granular experiments or models
where phase separation, accompanied by domain coarsening, is a relevant
phenomenon. We first elucidate the intrinsic non-equilibrium, or athermal,
nature of granular media. Thereafter, dilute systems, the so-called "granular
gases" are discussed: idealized kinetic models, such as the gas of inelastic
hard spheres in the cooling regime, are the optimal playground to study the
slow growth of correlated structures, e.g. shear patterns, vortices and
clusters. In fluidized experiments, liquid-gas or solid-gas separations have
been observed. In the case of monolayers of particles, phase coexistence and
coarsening appear in several different setups, with mechanical or electrostatic
energy input. Phenomenological models describe, even quantitatively, several
experimental measures, both for the coarsening dynamics and for the dynamic
transition between different granular phases. The origin of the underlying
bistability is in general related to negative compressibility from granular
hydrodynamics computations, even if the understanding of the mechanism is far
from complete. A relevant problem, with important industrial applications, is
related to the demixing or segregation of mixtures, for instance in rotating
tumblers or on horizontally vibrated plates. Finally, the problem of compaction
of highly dense granular materials, which has many important applications, is
usually described in terms of coarsening dynamics: there, bubbles of
mis-aligned grains evaporate, allowing the coalescence of optimally arranged
islands and a progressive reduction of total occupied volume.
