The last few years have seen major progress in harnessing on-chip photon-phonon interactions, leading to a wide range of demonstrations of new functionalities. Utilizing not only the optical response of a nonlinear waveguide-but also acoustic resonances-enables the realization of microwave devices with unprecedented performance, otherwise hard to achieve in all-optical processing schemes or electronically. Here, we overview on-chip stimulated Brillouin scattering (SBS) with special emphasis on microwave sources and microwave signal processing schemes. We review the different material platforms and structures for on-chip SBS, ranging from chalcogenide rib waveguides to hybrid silicon/silicon-nitride structures, high-Q photonic-phononic silica microresonators, and suspended silicon nanowires. We show that the paradigm shift in SBS research-from long length of fibers to chip-scale devices-is now moving toward fully integrated photonic-phononic CMOS chips.