Stochastic ODEs (SODEs) and PDEs (SPDEs) have become a significant modeling framework for problems ranging from biology to mathematical finance. However, the research in numerical algorithms for simulating such models are in their infancy compared to the deterministic counterparts. In this presentation we focus on an efficient algorithm for adaptive time-stepping. Methods to address this problem have been particularly underdeveloped since, unlike in adaptive deterministic methods, naive rejection sampling changes the distribution of the underlying Brownian path. An introduction will be given to show the importance of adaptive numerical algorithms and the shortcomings of the current algorithms. This will be followed by a detailed “chalkboard” derivation of a new general adaptive time-stepping algorithm. The purpose of this style will be to both further understand the correctness of the algorithm and display it in a way that will be intuitive for other practitioners to implement the algorithm in their own works. The talk is aimed at a general audience and will be mostly self-contained with no background in stochastic numerics required.