The modification of the optical properties of matter due to photon confinement in optical microcavities has been an active field of research in the last ten years. This review addresses the problem of Raman scattering in these optically confining structures. Two completely different regimes exist and will be discussed here. Firstly, a situation in which the action of the microcavity is basically to enhance, and to spatially and spectrally confine, the photon field, but otherwise the light-matter interaction process remains unaltered. This is the case when the laser and scattered photon energies are well below those of the excitoilic transitions in the structure, or when the coupling between the latter and the cavity mode can be treated in a ``weak coupling'' approximation. This regime will be labeled here as ``optical resonant Raman scattering''. And secondly, a ``strong-coupling'' regime in which exciton and cavity-photon modes cannot be treated separately, leading to coupled excitations, so-called cavity polaritons. In this second case, when the laser or scattered photons are tuned to the excitonic energies, and thus an electronic resonant Raman-scattering process is achieved, the Raman-scattering process has to be described in a fundamentally different way. This regime will be labeled as ``cavity-polariton-mediated Raman scattering''. The Chapter will begin, after a brief historical introduction, with a review of the fundamental properties of optical microcavities, and of the different strategies implemented to achieve double optical resonant Raman scattering in planar microcavities. A section will be then devoted to experimental results that highlight the different characteristics and potentialities of Raman scattering under optical confinement, including, in some detail, an analysis of the performance of these structures for Raman amplification. A subsequent section will present a series of research efforts devoted to the study of nanostructure phonon physics that rely on microcavities for Raman enhancement. In particular, emphasis will be given to recent investigations on acoustic cavities that parallel their optical counterparts but that, instead, confine hypersound in the GHz-THz range. The Chapter will then turn to a quite different topic, that of cavity-polariton-mediated scattering. The theory developed in the 1970s for bulk materials will be briefly introduced, and its modifications to account for photon confinement in planar structures will be addressed. Finally, a series of experiments that demonstrate the involvement of polaritons in the inelastic scattering of light in strongly coupled cavities will be reviewed. The Chapter will end with some conclusions and prospects for future developments on this subject. also a stimulated emission of coherent phonons. It is an interesting issue whether acoustic and optical cavities can contribute essential ingredients for the development of phonon ``lasers''. Acoustic cavities based on distributed Bragg reflectors as described here could provide the required feedback mechanism, while optical microcavities could be exploited to efficiently seed the stimulated-emission process. All the experiments reviewed here, and to the best of our knowledge all the reported investigations of Raman amplification in condensed-matter cavities, rely on planar one-dimensional confining structures. However, and in the same way as micrometer-size liquid droplets have led to enormous Raman gain, it is possible to conceive higher-dimensional optical confining structures that could be exploited for Raman amplification. These include pillars that, based on 1D cavities, achieve 3D optical confinement by lateral nanostructuring. Also whispering gallery modes in high-Q disk-like cavities can be a possible choice in the search of Raman signals from single, or a few, semiconductor dots. It would also be interesting to search for Raman amplification using high-Q modes related to defects and high density of states extended states in 2- and 3-dimensional photonic bandgap, devices. Last but not least, the reported experiments dealing with cavity-polariton-mediated scattering are extremely few, and the available theories quite crude. We believe that this remains an interesting and quite unexplored territory for research on a very basic and fundamental light-matter interaction process.