This review is devoted to integrated photonic platforms based on large band-gap semiconductors, alternatives to silicon photonics. The large electronic band gap of the material employed is chosen to address the specific needs of nonlinear optics, and, in particular, lower nonlinear losses and the capability of handling larger optical power densities. Moreover, these new platforms offer broader transmission spectra, extending to the visible spectral region, which is also required for other applications, particularly sensing and bio-related photonics. The focus is on nanoscale patterned waveguiding structures, which, owing to the tight confinement of light, have demonstrated a large nonlinear response. The third-order nonlinear response and the related parametric interactions will be considered here, encompassing four-wave mixing, phase-sensitive amplification, wavelength conversion, and also nonlinear pulse propagation and soliton dynamics. The comparison between different materials and waveguide design highlights specific features of photonic crystal waveguides.