Numerical resolution of optimal stopping problems has been an active area of research for more than two decades. Originally investigated in the context of American Option pricing, it has since metamorphosed into a field unto itself, with numerous wide-ranging applications and dozens of proposed approaches. A major strand, which is increasingly dominating the subject, is simulation-based methods rooted in the Monte Carlo paradigm. Developed in the late 1990s in [23] and [31] this framework remains without an agreed-upon name; we shall refer to it as Regression Monte Carlo (RMC). The main feature of RMC is its marriage of a probabilistic approach, namely simulation of the underlying stochastic state dynamics, and statistical tools for approximating the quantities of interest: the value and/or continuation functions, and the stopping region.