The high quality of actual epitaxial deposition techniques allowsthe engineering of electronic, photonic and phononic properties in semiconductor nanostructures for the design of novel multifunctional devices. Here we address the possibility to confine THz acoustic phonons in phonon cavities, and to enhance their coupling with light by embedding them within an optical microcavity. We briefly describe the parameters relevant for acoustic cavity design and phonon engineering in these devices, and we report the observation by high resolution Raman scattering of acoustic phonons confined in planar cavities with one to three confined acoustic modes. Raman efficiency enhancements above 105 are observed for the studied light-sound double resonators. Similarly to optical cavities, the acoustic resonators rely in periodic Bragg mirrors. Extending the parallel between optics and acoustics to other basic devices, we show that non-periodic nanostructures with tailored phononic properties in the THZ range can be designed using optimization algorithms, and characterized by Raman scattering.