Decision making in electricity markets under uncertainty has worldwide gained attention due to an increasing number of uncertain parameters associated to technology developments and market evolution. Hence, the market operator faces new challenges pertaining to technical and economic aspects of electricity markets. To tackle these challenges, appropriate models are necessary. This dissertation aims to analyze some of the challenges pertaining to the management in electricity markets under uncertainty and to provide the market operator with the models that enable it to make informed decisions in such uncertain market environments. In the context above, we categorize market operation problems into the following four groups. With the aim of obtaining informed day-ahead decisions in the presence of a number of intra-day markets and high renewable production, we propose a multi-stage stochastic clearing model, where the first stage represents the day-ahead market, n stages model n intra-day markets, and a final stage represents real-time operation. The proposed multi-stage clearing model considers not only different realizations of renewable power output, but also how these realizations evolve from day-ahead forecasts into real-time values, and allows flexibility for the contribution of renewable production in both the day-ahead and intra-day markets in form of scheduled productions and their adjustments. This improves the market outcomes and integration of renewable generation. With the purpose of obtaining marginal prices with cost-recovery features, we develop novel pricing methodologies in the presence of non-convexities and uncertainty in the market. These models minimize the duality gap of a stochastic non-convex clearing model and the dual problem of a relaxed version of this original model subject to primal constraints, dual constraints, cost-recovery constraints, and integrity constraints. The prices obtained deviate in the least possible manner from conventional marginal prices. This implies that a minimum deviation from the optimal value of social welfare is also guaranteed. Moreover, the new prices preserve the short-term economic efficiency and long-term cost recovery properties of marginal prices, while eliminating a need for uplifts. We provide insightful analyses on the impact of demand flexibility on the operational and economic aspects of the power system operation. We investigate how market prices are affected by flexible demands and what economic consequences are observed. For this purpose, we consider a system with high renewable production and a number of comparatively expensive fast-ramping units, which are flexible to react to the uncertainty pertaining to renewable power production. We investigate the role of flexible demands froman economic viewpoint, particularly the impact of flexible demands on demand revenues. Lastly, we develop a risk-neutral two-stage stochastic clearing model and a risk-averse one for reserve markets. We particularly focus on the Swiss reserve market, which consists of a weekly market with a gate closure one week ahead of real-time operation and a daily market with a gate closure two days ahead of real time. The decision-making problem consists of determining which amount of reserves to procure in the weekly market and which one in the daily market. If a risk-averse instance of this two-stage model is also proposed.