  We review the physics of hybrid optomechanical systems consisting of a
mechanical oscillator interacting with both a radiation mode and an additional
matter-like system. We concentrate on the cases embodied by either a single or
a multi-atom system (a Bose-Einstein condensate, in particular) and discuss a
wide range of physical effects, from passive mechanical cooling to the set-up
of multipartite entanglement, from optomechanical non-locality to the
achievement of non-classical states of a single mechanical mode. The reviewed
material showcases the viability of hybridised cavity optomechanical systems as
basic building blocks for quantum communication networks and quantum
state-engineering devices, possibly empowered by the use of quantum and optimal
control techniques. The results that we discuss are instrumental to the
promotion of hybrid optomechanical devices as promising experimental platforms
for the study of non-classicality at the genuine mesoscopic level.
