Properties of phonons-quanta of the crystal lattice vibrations-in graphene have recently attracted significant attention from the physics and engineering communities. Acoustic phonons are the main heat carriers in graphene near room temperature, while optical phonons are used for counting the number of atomic planes in Raman experiments with few-layer graphene. It was shown both theoretically and experimentally that transport properties of phonons, i.e. energy dispersion and scattering rates, are substantially different in a quasi-two-dimensional system such as graphene compared to the basal planes in graphite or three-dimensional bulk crystals. The unique nature of two-dimensional phonon transport translates into unusual heat conduction in graphene and related materials. In this review, we outline different theoretical approaches developed for phonon transport in graphene, discuss contributions of the in-plane and cross-plane phonon modes, and provide comparison with available experimental thermal conductivity data. Particular attention is given to analysis of recent results for the phonon thermal conductivity of single-layer graphene and few-layer graphene, and the effects of the strain, defects, and isotopes on phonon transport in these systems.