Planning is an essential part of intelligent behavior and a ubiquitous task for both humans and rational agents. One framework for planning in the presence of uncertainty is probabilistic planning, in which actions are described by a probability distribution over their possible outcomes. Probabilistic planning has been applied to different real-world scenarios such as public health, sustainability and robotics; however, the usage of probabilistic planning in practice is limited due to the poor performance of existing planners. In this thesis, we introduce a novel approach to effectively solve probabilistic planning problems by relaxing them into short-sighted problems. A short-sighted problem is a relaxed problem in which the state space of the original problem is pruned and artificial goals are added to heuristically estimate the cost of reaching an original goal from the pruned states. Differently from previously proposed relaxations, short-sighted problems maintain the original structure of actions and no restrictions are imposed in the maximum number of actions that can be executed. Therefore, the solutions for short-sighted problems take into consideration all the probabilistic outcomes of actions and their probabilities. In this thesis, we also study different criteria to generate short-sighted problems, i.e., how to prune the state space, and the relation between the obtained short-sighted models and previously proposed relaxation approaches. We present different planning algorithms that use short-sighted problems in order to solve probabilistic planning problems. These algorithms iteratively generate and execute optimal policies for short-sighted problems until the goal of the original problem is reached. We also formally analyze the introduced algorithms, focusing on their optimality guarantees with respect to the original probabilistic problem. Finally, this thesis contributes a rich empirical comparison between our algorithms and state-of-the-art probabilistic planners.