The concept of topology has yielded fruitful results since its introduction to photonics research. This thesis explores the extension of topological concepts into the realm of nonlinear photonics, building upon established principles in linear photonic systems. The investigation encompasses the study of different topological invariants, including those defined in far-field radiation and Bloch bands, which has led to intriguing effects such as backscattering immune propagation. In the context of nonlinear photonics, we first extend the notion of topological charges present in linear photonic systems. These topological charges, serving as vortex centers in the polarization direction of far-field radiation, indicate the existence of special non-radiative modes termed "bounded states in the continuum". The exploration reveals that nonlinear dipoles, specifically the second-harmonic dipoles of certain optical resonances, exhibit complete non-radiativity—a phenomenon termed "resonance-forbidden second harmonic generation". Moving forward, we shift our focus to topology defined based on photonic bands within periodic-driven nonlinear photonic systems. Here, we investigate Floquet bands and demonstrate the potential to break time-reversal symmetry through a circularly polarized pump beam. This breakthrough allows for the realization of a Floquet Chern insulator in a two-dimensional system. A concrete design is presented, and experimental demonstrations are carried out with a pump-probe setup, confirming the system's entry into what we term a "Floquet strong coupling regime." Finally, we introduce a compound space-time symmetry in a driven nonlinear photonic system. This unique symmetry is shown to protect a high-order topological phase—a Floquet quadrupole phase. Numerical demonstrations illustrate key consequences of this nontrivial bulk moment at the interfaces, including the emergence of corner states and filling anomalies. In conclusion, we present a comprehensive exploration of topological concepts in nonlinear photonics, combining theoretical frameworks with experimental validations. The potential real-life applications of these findings further enlighten the significance of topology in advancing the field.