  Two-dimensional (2D) van der Waals (vdW) materials have extraordinary thermal
properties due to the effect of quantum confinement, making them promising for
thermoelectric energy conversion and thermal management in microelectronic
devices. In this review, the mechanism of phonon anharmonicity originating from
three- and four-phonon interactions is derived. The phonon anharmonicity of 2D
vdW materials, involving the Gr\"uneisen parameter, phonon lifetime, and
thermal conductivity, is summarized and derived in detail. The size-dependent
thermal conductivity of representative 2D vdW materials is discussed
experimentally and theoretically. This review will present fundamental and
advanced knowledge on how to evaluate the phonon anharmonicity in 2D vdW
materials, which will aid the design of new structures and materials for
applications related to energy transfer and conversion.
