Harnessing nonlinear optical effects in a photonic chip scale has been proven useful for a number of key applications in optical communications. Microwave photonics can also benefit from the adoption of such a technology, creating a new concept of nonlinear integrated microwave photonics. Here, we discuss the potential of on-chip nonlinear processing towards the creation of robust and multifunctional microwave photonic (MWP) processors. We also highlight key recent results in the field, including frequency agile MWP filters and ultrawideband signal generators.