Stochastic processes are ubiquitous in many different fields such as molecular dynamics, population genetics, finance, environmental models, turbulence and many more. The increased use of stochastic processes in models poses challenges in fitting these models to the data and finding estimators that converge at optimal rates and are efficient. The stochastic processes are often only observed at discrete times or locations and this leads to difficult nonlinear inverse problems for the parametric and nonparametric estimation of stochastic processes. This session covers a wide variety of different time-continuous stochastic processes and presents state-of-the-art methods and results for diffusion processes, jump processes and stochastic PDEs. Results on minimax rates of convergence and on central limit theorems for the constructed estimators are presented.