  The form of energy termed heat that typically derives from lattice
vibrations, i.e. the phonons, is usually considered as waste energy and,
moreover, deleterious to information processing. However, with this colloquium,
we attempt to rebut this common view: By use of tailored models we demonstrate
that phonons can be manipulated like electrons and photons can, thus enabling
controlled heat transport. Moreover, we explain that phonons can be put to
beneficial use to carry and process information. In a first part we present
ways to control heat transport and how to process information for physical
systems which are driven by a temperature bias. Particularly, we put forward
the toolkit of familiar electronic analogs for exercising phononics; i.e.
phononic devices which act as thermal diodes, thermal transistors, thermal
logic gates and thermal memories, etc.. These concepts are then put to work to
transport, control and rectify heat in physical realistic nanosystems by
devising practical designs of hybrid nanostructures that permit the operation
of functional phononic devices and, as well, report first experimental
realizations. Next, we discuss yet richer possibilities to manipulate heat flow
by use of time varying thermal bath temperatures or various other external
fields. These give rise to a plenty of intriguing phononic nonequilibrium
phenomena as for example the directed shuttling of heat, a geometrical phase
induced heat pumping, or the phonon Hall effect, that all may find its way into
operation with electronic analogs.
