Coherent interactions between light and sound have been of significant interest since the invention of the laser. Stimulated Brillouin scattering (SBS) is a type of coherent interaction where light is scattered from optically generated acoustic waves. SBS is a powerful tool for optical and microwave signal processing, with applications ranging from telecommunications and Radar, to spatial sensing and microscopy. Over the last decade there has been increasing interest in the investigation of Brillouin scattering at device scales smaller than the wavelength of light. New interactions with the waveguide boundaries in these systems are capable of altering the strength of SBS, from complete suppression to orders of magnitude increases. The landmark demonstration of Brillouin scattering in planar waveguides, just six years ago, represents a new frontier for this field. This work explores the effective generation and harnessing of stimulated Brillouin scattering within modern photonic circuits. After establishing the foundations of linear and nonlinear optical circuits, we investigate the Brillouin processes available in multimode waveguides. We experimentally demonstrate giant Brillouin amplification using spiral waveguides consisting of soft-glass materials. We then integrate this soft-glass onto the standard platform for photonic circuits, silicon on insulator, without any reduction in performance. We apply these advanced devices to the field of microwave photonics and create high suppression microwave filters with functionality far beyond traditional electronic circuits. This thesis is a significant step towards Brillouin enabled integrated photonic processors
