In this review we present an overview of the progress made in recent years in the field of integrated silicon-on-insulator (SOI) waveguide photonics with a strong emphasis on third-order nonlinear optical processes. Although the focus is on simple waveguide structures the utilization of complex structures such as microring resonators and photonic crystal structures is briefly discussed as well. Several fabrication methods are explained and methods which improve optical loss, coupling efficiency and polarization dependence are presented.As the demand for bandwidth increases communication systems are forced to use higher bit rates to accommodate the load. A consequence of high-bit-rate systems is that they require short pulses where the importance of waveguide dispersion tailoring becomes increasingly important. The impact of short pulses on the efficiency of all-optical processes is discussed and recent accomplishments in this field are presented. Numerical results of femtosecond, picosecond and nanosecond pulse propagation in SOI waveguides are compared to provide an insight into the physical processes that dominate at these different time scales. In this work we focus on two-photon absorption (TPA), free-carrier absorption (FCA), plasma dispersion and the optical Kerr effect. After describing these nonlinear effects, some other important all-optical processes based on plasma dispersion and the Kerr effect are described, namely cross-absorption modulation (XAM), self-phase modulation (SPM), cross-phase modulation (XPM), four-wave mixing (FWM) and stimulated Raman scattering (SRS). The latter provides the best hope for practical and/or commercial applications and finds its use in amplification and lasing. Furthermore, we present some guidelines for efficient numerical modelling of propagation in SOI waveguides. This review is a good starting point for those who are new in this hot and rapidly emerging field and gives an overview of important considerations that need to be taken into account when designing, fabricating and characterizing SOI waveguides for ultrafast third-order nonlinear all-optical processing.