In this Colloquium recent advances in the field of quantum heat transport are reviewed. This topic has been investigated theoretically for several decades, but only during the past 20 years have experiments on various mesoscopic systems become feasible. A summary of the theoretical basis for describing heat transport in one-dimensional channels is first provided. The main experimental investigations of quantized heat conductance due to phonons, photons, electrons, and anyons in such channels are then presented. These experiments are important for understanding the fundamental processes that underlie the concept of a heat conductance quantum for a single channel. An illustration of how one can control the quantum heat transport by means of electric and magnetic fields, and how such tunable heat currents can be useful in devices, is first given. This lays the basis for realizing various thermal device components such as quantum heat valves, rectifiers, heat engines, refrigerators, and calorimeters. Also of interest are fluctuations of quantum heat currents, both for fundamental reasons and for optimizing the most sensitive thermal detectors; at the end of the Colloquium the status of research on this topic is given.

• Received 15 February 2021

DOI:https://doi.org/10.1103/RevModPhys.93.041001