Phonons, i.e. quanta of lattice vibrations, manifest themselves in all electrical, thermal, and optical phenomena in semiconductors and other material systems. Reduction of the size of electronic devices below the acoustic phonon mean free path creates a new situation for the phonons propagation and interaction. From one side, it may complicate heat removal from the downscaled devices. From the other side, it opens up an opportunity for engineering phonon spectrum in nanostructured materials, and achieving enhanced operation of nanoscale devices. In the paper the author presents brief description of the theoretical development of the nanoscale phonon engineering concept for multilayered nanostructures i.e. concept of the tuning the phonon spectrum in the acoustically mismatched nano- and heterostructures in order to change the ability of semiconductors to conduct heat or electric current. He also reviews the theoretical and experimental results of heat conduction in monolayer and few-layer graphene, obtained for the first time by the physists from University of California – Riverside and Moldova State University