  The emerging field of phase-coherent caloritronics (from the Latin word
"calor", i.e., heat) is based on the possibility to control heat currents using
the phase difference of the superconducting order parameter. The goal is to
design and implement thermal devices able to master energy transfer with a
degree of accuracy approaching the one reached for charge transport by
contemporary electronic components. This can be obtained by exploiting the
macroscopic quantum coherence intrinsic to superconducting condensates, which
manifests itself through the Josephson and the proximity effect. Here, we
review recent experimental results obtained in the realization of heat
interferometers and thermal rectifiers, and discuss a few proposals for exotic
non-linear phase-coherent caloritronic devices, such as thermal transistors,
solid-state memories, phase-coherent heat splitters, microwave refrigerators,
thermal engines and heat valves. Besides being very attractive from the
fundamental physics point of view, these systems are expected to have a vast
impact on many cryogenic microcircuits requiring energy management, and
possibly lay the first stone for the foundation of electronic thermal logic.

Mesoscale and Nanoscale Physics;Superconductivity