Photonic platforms with excellent nonlinear optical characteristics are very important to improve the devices' performance parameters such as integration, modulation speeds and working bandwidths for all-optical signal processing. The traditional processing technology of photonic platforms based on silicon, silicon nitride and silicon oxide is mature, but the nonlinear function of these optical platforms is limited due to the characteristics of materials; Although two-dimensional (2D) materials possess excellent nonlinear optical properties, their nonlinear potentials cannot be fully utilized because of their atomic layer thickness. Integrating 2D materials with mature photonic platforms can significantly improve the interaction between light and matter, give full play to the potentials of 2D materials in the field of nonlinear optics, and improve the nonlinear optical performances of the integrated platforms on the basis of fully utilizing the mature processing technology of the photonic platforms. Based on the above ideas, starting from the basic principle of nonlinear optics (Section 2), this review combs the research progress of various nonlinear photonic platforms (resonators, metasurfaces, optical fibers, on-chip waveguides, etc.) heterogeneously integrated with 2D materials, realized by traditional transfer methods (Section 3) and emerging direct-growth methods (Section 4) in recent years, and the introduction is divided into second-order and third-order nonlinearity. Comparing with the transfer methods, the advantages of using direct-growth methods to realize the heterogeneous integration of 2D materials and photonic platforms for the study of nonlinear optics are expounded, and the technical difficulties to be overcome in preparing the actual devices are also pointed. In the future, we can try to grow 2D materials directly onto the surfaces of various cavities to study the enhancement of second-order nonlinearity; we can also try to grow 2D materials directly onto the on-chip waveguides or microrings to study the enhancement of third-order nonlinearity. Generally speaking, the research on integrated nonlinearity by directly growing 2D materials onto various photonic structures has aroused great interest of researchers in this field. As time goes on, breakthrough progress will be made in this field, and technical problems such as continuous growth of high-quality 2D materials onto photonic structures and wafer-level large-scale preparation will be broken through, further improving the performance parameters of chips and laying a good foundation for optical communication, signal processing, optical sensing, all-optical computing, quantum technology and so on.