Power systems present a variety of characteristics which makes their operation challenging. One complication of power system operation is the necessity of the overall structure to react to uncertain events, which are becoming increasingly important as the energy transition results in the expansion of renewable technologies, and decision makers are faced with the task of reacting to unforeseen events. From a methodological point of view, this novel energy landscape implies that the scale of the scheduling and planning problems at hand is becoming increasingly large, which poses challenges to state-of-the-art optimization techniques. This dissertation aims at proposing novel algorithmic schemes, supported by high performance computing, that help with addressing the increasingly relevant paradigm of optimization under uncertainty in power systems. The first part of this thesis considers a class of problems referred to as multistage stochastic optimization problems. We specifically focus on the longterm hydrothermal scheduling problem. This class of problems is known to be difficult to tackle. We build upon the SDDP algorithm, and extend the algorithm through high performance computing. We specifically exploit high performance computing in order to study a variety of strategies for speeding up the overall algorithmic performance. We benchmark our proposed algorithmic scheme against PSR SDDP, an industrial scale implementation, and report favorable performance comparisons. Furthermore, we discuss the connections between our techniques and the reinforcement learning framework. The second part of this dissertation considers the ongoing European Resource Adequacy Assessment. This study aims at measuring the capacity of the power system network to react to future uncertain conditions. Institutionally, the adequacy concerns identified through such a study support Member States in determining the need for national capacity mechanisms. A critical methodological step of the overall study is to determine the generation capacity expansion opportunities as well as decommissioning decisions of existing capacity that will occur in the upcoming years, thus naturally leading us to a framework of optimization under uncertainty. As a first step to address the problem, this thesis considers the single-year setting used for the 2021 version of the study. We leverage the two-stage stochastic programming framework, and propose parallel computing algorithmic schemes for tackling the problem.