Harnessing nonlinear optical effects in a photonic chip scale has been proven useful for a number of key applications in optical communications. Microwave photonics (MWP) can also benefit from the adoption of such a technology, creating a new concept of nonlinear integrated MWP. Here, we look at the potential of using nonlinear optical effects in a chip scale to enable RF signal processing with enhanced performance. We review a number of recent results in this field, with particular focus on the creation of frequency agile and high suppression microwave bandstop filters using on-chip stimulated Brillouin scattering. We also discuss the future prospect of nonlinear integrated MWP to enable a general purpose, programmable analog signal processor, as well as compact, high performance active microwave filters with enhanced energy efficiency.