  Heat conduction by phonons is a ubiquitous process that incorporates a wide
range of physics and plays an essential role in applications ranging from space
power generation to LED lighting. Heat conduction has been studied for over two
hundred years, yet many microscopic aspects of heat conduction have remained
unclear in most crystalline solids, including which phonons carry heat and how
natural and artificial structures scatter specific phonons. Fortunately, recent
advances in both computation and experiment are enabling an unprecedented
microscopic view of thermal transport by phonons. In this topical review, we
provide an overview of these methods, the insights they are providing, and
their impact on the science and engineering of heat conduction.
