There are many intriguing physical phenomena that are associated with topological features --- global properties that are not discernible locally. The best-known examples are quantum Hall effects in electronic systems, where insensitivity to local properties manifests itself as conductance through edge states which are insensitive to defects and disorder. In the talk, we first discuss how similar physics can be explored with photons; specifically, how various topological models can be simulated in various photonics systems, from ring resonators to photonic crystals. We then discuss that the integration of strong optical nonlinearity can lead to unique bosonic phenomena, such as a topological source of quantum light and chiral quantum optics. These results may enable the development of classical and quantum optical devices with built-in protection for next-generation optoelectronic and quantum technologies. In the end, we discuss an emerging field at the interface of quantum optics and correlated electron systems, with the goal of creating and manipulating many-body states of light-matter hybrids with new functionalities, such as high-Tc superconductors.