Dynamic decision-making under uncertainty has a long and distinguished history in opera-tions research. Due to the curse of dimensionality, solution schemes that na ̈ıvely partition ordiscretize the support of the random problem parameters are limited to small and medium-sizedproblems, or they require restrictive modeling assumptions (e.g., absence of recourse actions).In the last few decades, several solution techniques have been proposed that aim to alleviate thecurse of dimensionality. Amongst these is thedecision rule approach, which faithfully modelsthe random process and instead approximates the feasible region of the decision problem. Inthis paper, we survey the major theoretical findings relating to this approach, and we investigateits potential in two applications areas.