**1. Introduction**

Graphene, a two-dimensional (2D) atomic thin honeycomb lattice, exhibits numerous striking physical properties, and can, in principle, be considered as an elementary building block for all carbon allotropes. Ever since the recent developments in 2004, the field of graphene research took off rapidly. These developments in the science of graphene prompted an unprecedented

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surge of activity and demonstration of new physical phenomena. Despite its success, gra‐ phene still faces some severe problems in its nature of semi-metal or zero band-gap semicon‐ ductor and its incompatibility with the current Si-based semiconductor technology. Given that the honeycomb geometry is related to some of the exceptional properties of graphene, there is strong motivation to investigate whether changing carbon to other atom type might give rise to novel physical phenomena as well. An intuitive idea is to study similar 2D materials, such as siliceneandphosphorene.Actually, silicene,theSicounterpartofgraphene,cansolvetheabovementioned problems smoothly and thus has received intense interest lately. Given the fact that thermal transport plays a critical role in many applications such as heat dissipation in nanoe‐ lectronics and thermoelectric energy conversion, there has been an emerging demand in characterizing thermal (mainly phonons) transport property of silicene structures. Moreover, research results have shown that silicene exhibits a few novel thermal transport properties, which are fundamentally different from that of graphene, despite the similarity of their honeycomb lattice structure. Therefore, the abnormal physical property, primarily stemming from its unique low buckling structure, may enable silicene to open up entirely new possibili‐ ties for revolutionary electronic devices and energy conversion materials.

With the state of the art, this book chapter aims to present theoretical investigations of thermal transport of broad 2D nanostructures in various forms, which have been carried out in our research group in the past few years. Heat transfer in such structures is not only directly relevant to optimizing the device performance such as improved thermal manage‐ ment for nanoelectronics and thermoelectric energy conversion efficiency, but also is a scientifically fundamental problem for many other similar two-dimensional systems (**Figure 1**).

**Figure 1.** Comparison of the crystal structures (top view and side view) among (a) graphene, (b) silicene, and (c) phos‐ phorene. Graphene possesses perfect planar structure, silicene possesses low buckling structure, and phosphorene possesses pucker (hinge-like) structure.
