The following paper reports the lecture delivered by Prof. Alexander Gaeta, from the School of Applied and Engineering Physics, Cornell University, Ithaca, USA, and describes recent developments in the field of nonlinear photonics in chip-based structures, focusing on silicon-based nanowaveguides and resonators. At first we describe the main physical effects underpinning nonlinear optics in integrated structure, arising from the third-order (Kerr) nonlinearity, such as self-phase modulation, four-wave mixing, and parametric oscillation. We show that, after suitably engineering the waveguide dispersion, silicon-based devices can produce supercontinuum light spanning more than an octave, frequency combs of more than 100 THz bandwidth, pulses of nearly 100 femtosecond duration, and photon pairs for quantum optics applications.