In recent years, two-dimensional atomic-level thickness crystal materials have attracted widespread interest such as graphene, hexagonal boron nitride (h-BN), silicene, germanium, black phosphorus (BP), transition metal sulfides and so on. These graphene-like two-dimensional (2D) materials have a lot of excellent characteristics such as high specific surface area and high Young's modulus, and many potential applications in diverse areas such as photo-electricity, catalysts, and transistors. In this review, we introduced the synthesis, structure, properties, and applications of graphene, h-BN, and their heterostructures, especially focused on their mechanical, optical, thermal, electric, and magneticproperties. Finally, we present the outlooks and perspectives for these types of excellent 2D materials and their potential applications. Fig. 42 Schematic of the structures of: (A) an in-plane pressure sensor and (B) a tunnelling pressure sensor. Transmission spectra of: (C) the in-plane sensor and (D) the tunnelling sensor as functions of electron energy with different external pressure. 213This journal is