In this report we review the results of our investigation of thermal conductivity of graphene. It was recently discovered experimentally that thermal conductivity of suspended graphene flakes is extremely high and can exceeds that of bulk graphite and carbon nanotubes [1]. It has been found that the near room temperature (RT) thermal conductivity of the single layer suspended graphene is in the range from ~3000 Wm-1K-1 to 5300 Wm-1K-1 depending on the size (width and length) of the graphene flakes [1] and it decreases to values of bulk graphite in-plane thermal conductivity with increasing the number of the atomic planes [2]. In order to explain such high values of the thermal conductivity of “free” graphene and the thermal conductivity dependence on the number of atomic layers monolayers number we performed rigorous calculations [2-3]. The phonon dispersion for all polarizations and crystallographic directions in graphene lattice was obtained using VFF method. The three-phonon Umklapp processes were treated accounting for all phonon relaxation channels allowed by the momentum and energy conservation laws. It was found that the near RT thermal conductivity of single layer graphene, calculated with a realistic Gruneisen parameter, is 2000 – 5000 Wm-1K-1 depending on the defect concentration and roughness of the edges [3-4]. The obtained theoretical values are in the excellent agreement with the experimental data [1-2]. The thermal conductivity decreases with increasing number of atomic layers due to the cross-plane coupling of the low-energy phonons and changes in the phonon Umklapp scattering [2]. We also investigated the dependence of the thermal conductivity in graphene [4] on the flake length L and established that RT thermal conductivity increases with increasing L up to a certain length (see Fig. 1). For larger L the higher-order phonon processes lead to the thermal conductivity saturation. Figure 1: Calculated and measured thermal conductivity of graphene flakes. Experimental data is after A.A. Balandin et al. [1-2]. Note that in real structures the thermal conductivity will also be limited by the extrinsic effects such as the scattering on grain boundaries, substrate scattering, etc.