Two-dimensional (2D) materials are widely used in microelectronic devices due to their excellent optical, electrical, and mechanical properties. The performance and reliability of microelectronic devices based 2D materials are affected by heat dissipation performance, which can be evaluated by studying the thermal conductivity of 2D materials. Currently, many theoretical and experimental methods have been developed to characterize the thermal conductivity of 2D materials. In this paper, firstly, typical theoretical methods, such as molecular dynamics, phonon Boltzmann transport equation, and atomic Green’s function method, are introduced and compared. Then, experimental methods, such as suspended micro-bridge, 3ω, time-domain thermal reflectance and Raman methods, are systematically and critically reviewed. In addition, the physical factors affecting the thermal conductivity of 2D materials are discussed. At last, future prospects for both theoretical and experimental thermal conductivity characterization of 2D materials is given. This paper provides an in-depth understanding of the existing thermal conductivity measurement methods of 2D materials, which has guiding significance for the application of 2D materials in micro/nanodevices.