The description of phonon heat conduction is typically based on Fourier's diffusion theory. However, due to factors such as spatial confinement, dimensionality reduction, and disorder, there exist phonon transport phenomena that deviate from the classical Fourier diffusion theory. Over the past few decades, most of the non-Fourier phonon transport phenomena have been focused on the classical size effects that lead to a reduction in thermal conductivity. Additionally, researchers have observed other phenomena, often at the micro- and nanoscales. These include coherent thermal transport, phonon wave behavior, predictions and observations of phonon hydrodynamics, quantum thermal conduction, and Anderson localization. These advancements have revealed a rich landscape of phonon heat conduction, which will be beneficial for applications and control of materials' thermal transport.
