Demonstration of continuously tunable delay, lownoise lasers, dynamically controlled gratings, and optical phase shifting using the stimulated Brillouin scattering (SBS) process has lead to the emergence of SBS as a promising technology for microwave photonics. On-chip realization of SBS enables photonic integration of microwave photonic signal processing and offers significantly enhanced performance and improved efficiency. On-chip stimulated Brillouin scattering is reviewed in the context of slow-light based tunable delay, low-noise narrow linewidth lasers and filtering for integrated microwave photonics. A discussion on key material and device properties, necessary to enable on-chip Brillouin scattering using both the single-pass and resonator geometry, is presented along with an outlook for photonic integration of microwave signal processing and generation in other platforms.