Phonons, i.e., quanta of lattice vibrations, manifest themselves practically 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 phonon propagation and interaction. From one side, it complicates heat removal from the downscaled devices. From the other side, it opens up an exciting opportunity for engineering phonon spectrum in nanostructured materials and achieving enhanced operation of nanodevices. This paper reviews the development of the phonon engineering concept and discusses its device applications. The review focuses on methods of tuning the phonon spectrum in acoustically mismatched nano- and heterostructures in order to change the phonon thermal conductivity and electron mobility. New approaches for the electron-phonon scattering rates suppression, formation of the phonon stopbands and phonon focusing are also discussed. The last section addresses the phonon engineering issues in biological and hybrid bio-inorganic nanostructures.