  Dense suspensions of particles are relevant to many applications and are a
key platform for developing a fundamental physics of out-of-equilibrium
systems. They present challenging flow properties, apparently turning from
liquid to solid upon small changes in composition or, intriguingly, in the
driving forces applied to them. The emergent physics close to the ubiquitous
jamming transition (and to some extent the glass and gelation transitions)
provides common principles with which to achieve a consistent interpretation of
a vast set of phenomena reported in the literature. In light of this, we review
the current state of understanding regarding the relation between the physics
at the particle scale and the rheology at the macroscopic scale. We further
show how this perspective opens new avenues for the development of continuum
models for dense suspensions.
