  A discovery of the unusual thermal properties of graphene stimulated
experimental, theoretical and computational research directed at understanding
phonon transport and thermal conduction in two-dimensional material systems. We
provide a critical review of recent results in the graphene thermal field
focusing on phonon dispersion, specific heat, thermal conductivity, and
comparison of different models and computational approaches. The correlation
between the phonon spectrum in graphene-based materials and the heat conduction
properties is analyzed in details. The effects of the atomic plane rotations in
bilayer graphene, isotope engineering, and relative contributions of different
phonon dispersion branches are discussed. For readers' convenience, the
summaries of main experimental and theoretical results on thermal conductivity
as well as phonon mode contributions to thermal transport are provided in the
form of comprehensive annotated tables.
