Phonons, i.e. quanta of the crystal lattice vibrations, affect all physical processes in solids. They limit the electron mobility near room temperature (RT), and affect optical properties of crystalline materials. Spatial confinement of acoustic phonons in nanostructures strongly affects their phonon energy dispersions. It modifies phonon properties such as phonon group velocity, polarization, density of states, and changes the way acoustic phonons interact with other phonons, defects and electrons [1]. Such changes create opportunities for engineering phonon spectrum in nanostructures for improving their electrical or thermal properties. Acoustic phonons are the main heat carriers in carbon materials [2]. Although graphite reveals many metal characteristics, its heat transport is dominated by phonons owing the exceptionally strong sp2 covalent bonding of its lattice. The thermal conductivity of various allotropes of carbon span an extraordinary large range – of over five orders of magnitude – from ~0.01 Wm-1K-1 in amorphous carbon to above 2000 Wm-1K-1 in diamond or graphite at RT [2]. In 2007, the first measurements of the thermal conductivity of graphene carried out by Prof. A. Balandin’s group at UC Riverside revealed unusually high values of thermal conductivity κ~3000 – 5000 Wm-1K-1 at RT [3-4]. The values measured for the high-quality large suspended graphene samples (length above 10 μm) were exceeding those for basal planes of graphite [3-4]. The experimental observation was explained theoretically by the specifics of the two-dimensional (2D) phonon transport [5,6]. The low-energy acoustic phonons in graphene, which make substantial contribution to heat conduction, have extraordinary large MFP [4]. The anharmonic scattering in 2D graphene is very weak for such phonons. The large values of thermal conductivity and 2D phonon density of states make graphene an ideal material for phonon engineering. In this talk we discuss different possibilities of phonon engineering in graphene and twisted graphene. We briefly review available theoretical and experimental results on the thermal conductivity of these materials, focusing on unusual strong dependence of thermal conductivity on flake’s size and shape, concentration of defects and edge roughness.