B. L. Hu summarizes current research in stochastic semiclassical gravity, proposing it as a generalization of semiclassical gravity with a stochastic source term from quantum field fluctuations. This theory, which includes the Einstein-Langevin equation, aims to describe the backreaction of quantum fields on spacetime and the emergence of classical structures from quantum processes. The theory treats semiclassical gravity as mesoscopic physics, with general relativity as the hydrodynamic limit of quantum spacetime structures. Key concepts include stochasticity, collectivity, and correlations, as well as dissipation, fluctuations, and decoherence. The paper discusses how stochastic behavior at low energy can carry information about high-energy physics, and how quantum fluctuations can induce metric fluctuations. It also explores applications to black hole fluctuations, structure formation in cosmology, and thermal field theories. The paper emphasizes the importance of the fluctuation-dissipation relation and the role of noise in the transition from quantum to classical physics. It also discusses the implications of stochastic gravity for quantum gravity, suggesting that it provides a bridge between semiclassical and quantum gravity by incorporating quantum field fluctuations into spacetime dynamics. The paper concludes with suggestions for further research, including the study of higher-order correlation functions and the application of stochastic gravity to black hole and cosmological problems.B. L. Hu summarizes current research in stochastic semiclassical gravity, proposing it as a generalization of semiclassical gravity with a stochastic source term from quantum field fluctuations. This theory, which includes the Einstein-Langevin equation, aims to describe the backreaction of quantum fields on spacetime and the emergence of classical structures from quantum processes. The theory treats semiclassical gravity as mesoscopic physics, with general relativity as the hydrodynamic limit of quantum spacetime structures. Key concepts include stochasticity, collectivity, and correlations, as well as dissipation, fluctuations, and decoherence. The paper discusses how stochastic behavior at low energy can carry information about high-energy physics, and how quantum fluctuations can induce metric fluctuations. It also explores applications to black hole fluctuations, structure formation in cosmology, and thermal field theories. The paper emphasizes the importance of the fluctuation-dissipation relation and the role of noise in the transition from quantum to classical physics. It also discusses the implications of stochastic gravity for quantum gravity, suggesting that it provides a bridge between semiclassical and quantum gravity by incorporating quantum field fluctuations into spacetime dynamics. The paper concludes with suggestions for further research, including the study of higher-order correlation functions and the application of stochastic gravity to black hole and cosmological problems.