  Recently, there have been increasing interests in phonon thermal transport in
low dimensional materials, due to the crucial importance for dissipating and
managing heat in micro and nano electronic devices. Significant progresses have
been achieved for one-dimensional (1D) systems both theoretically and
experimentally. However, the study of heat conduction in two-dimensional (2D)
systems is still in its infancy due to the limited availability of 2D materials
and the technical challenges in fabricating suspended samples suitable for
thermal measurements. In this review, we outline different experimental
techniques and theoretical approaches for phonon thermal transport in 2D
materials, discuss the problems and challenges in phonon thermal transport
measurements and provide comparison between existing experimental data. Special
focus will be given to the effects of the size, dimensionality, anisotropy and
mode contributions in the novel 2D systems including graphene, boron nitride,
MoS2, black phosphorous, silicene etc.
