In this Chapter we discuss applications of GPs to optimal stopping problems, especially pricing of American-style options. We consider the use of GPs to learn continuation values connecting to the Regression Monte Carlo framework for simulation-based solvers of optimal stopping. We adopt the discrete-time paradigm of Bermudan options that allow for exercise at a predetermined collection of K (discrete) times \(\mathcal {T}=\{t_k: k=0,1,2,\ldots ,K,\ t_K=T\}\) up to T. The Chapter highlights the specific features of Optimal Stopping Problems to pinpoint what aspects of the GP model are critical for successful implementation, such as the recursive nature of the function approximation tasks and the importance of noise modeling. Section 5.2 considers active learning and adaptive batching approaches to construct more efficient GP surrogates. This Chapter is accompanied by an R notebook illustrating a construction of GP surrogates for one- and two-dimensional Bermudan option valuation.