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We compute the thermal conductivity of graphene and graphite by solving the Boltzmann Transport Equation(BTE)for phonons [1],with the phonon-phonon collision rates obtained from density-functional perturbation theory.We find that the single-mode relaxation time approximation (SMRTA)cannot describe the in-plane heat transport correctly,underestimating by at least one order of magnitude the thermal conductivity and heat mean free paths.Instead,we show that the exact self-consistent solution of the BTE provides results in excellent agreement with experimental measurements [2].The shortcomings of the SMRTA lie in the assumption that heat flow is transferred only by individual phonon excitations,whereas in layered materials the transport can only be explained in terms of collective phonon excitations.The characteristic length of these collective excitations is often comparable with that of the experimental sample-as a result,even Fouriers law become questionable,since its statistical nature makes it applicable only to systems larger than a few mean free paths.Finally,we analyze in details the effect of isotopes and strain,often deemed to be responsible for discrepancies between experiments [2].