Advances in integrated optoelectronics and nanophotonics have been very rich in recent years. These include the spectacular developments of nonlinear group four photonic platforms as well as the integration of components and functions based on III-V semiconductor materials. One of the strongest trends for the future is the development of all-optical signal processing functions within integrated, compact, low-loss devices, paving the way for new applications. This approach, relying on materials, components and the integration of optical functions, is based on a wide range of exciting physical phenomena, exploiting the nonlinear optical response of materials for the generation of frequency combs, the conversion of light wavelength, the generation of supercontinuum radiation, and many other phenomena exploiting the unprecedented power of light control by waves. This special issue has drawn a critical overview of the recent and significant burgeoning advances in the field, as well as to identify the next technological and scientific milestones to come for the development of integrated nonlinear photonics. Meanwhile, it aims to shed light on the interdisciplinary dimension of the work carried out in the field, based, for example, on the control of optical waves by acoustic waves, opening the way to the fields of nonlinear optomechanics and optoacoustics.