Nonlinear photonic-crystal nanoresonators improve the performance opf nonlinear optical devices to such an extent that their corresponding operation powers and switching times are suitable for their implementation in realistic integrated optical devices. Here we review three different nonlinear optical phenomena that can be strongly enhanced in photonic crystal nanocavities. First, we discuss in detail a system in which this enhancement has been successfully demonstrated both theroretically and experimentally, namely, a photonic crystal cavity showing optical bistability properties. In this part, we also present the physical basis for this dramatic improvement with respect to the case of traditional nonlinear devices based on nonlinear Fabry-Perot etalons. Secondly, we shown how nonlinear photonic crystal cavities can also be used to obtain complete second-harmonic frequency conversion at very low input powers. Finally, we demonstrate that the nonlinear susceptibility of a material can be strongly modified via the so-called Purcell effect present in the resonant cavities under study.