As an important part of modern optics and photonics, nonlinear optics plays a significant role in both research and application. However, at the micrometer and nanometer scales, the nonlinear optical response of a material is generally weak owing to the inherent nonlinear susceptibility and limited interaction length of the material; this restricts the development of integrated nanoscale nonlinear optoelectronic devices. In recent years, by taking advantage of the ability of surface plasmons to confine the electromagnetic field into a subwavelength volume, researchers have observed the nonlinear optical effects in the micro/nano-structures under the weak excitation light. This has gradually led to the formation of a new research field: nonlinear plasmonics. Different from previous review articles that have focused more on the nonlinear optical properties of the plasmonic metal nanostructures, in this paper, we emphasize the recent progress of nonlinear optical effects in hybrid metal-dielectric systems. First, we introduce the related properties and theoretical background of plasmonics and nonlinear optics; then, we summarize researches related to nonlinear optical enhancement effects in zero-dimensional hybrid systems, nonlinear effects in one-dimensional hybrid systems, nonlinear plasmonics in two-dimensional graphene, respectively. Finally, we discuss future research directions in the field of nonlinear plasmonics and significant opportunities and challenges.