Planning under uncertainty is one of the most general and hardest problems considered in the area of planning. Uncertainty can take the form of incomplete information, wrong information, multiple action outcomes, and varying action durations. My doctoral thesis concentrates on planning with incomplete knowledge and multiple action outcomes, specifically conformant planning and contingent planning. These problems have attracted the attention of many researchers, resulting in numerous sophisticated planners of different approaches. However, those planners cannot scale up well on the size of problems, mostly due to the representation methods employed in the planners. The doctoral research work provides a systematic methodology for dealing with planning under uncertainty, focusing on the representation of belief states that can be used in a forward search paradigm in the belief space for solutions. A good representation should be compact so that a planner implementing it can perform and scale up well as the larger the formulae, the more the computation and the more the memory consumption (i.e., the slower the system and the less the scalability). On the other hand, it should also have properties that allow for definition of an efficient transition function for computing successor belief states, e.g., checking satisfaction in a DNF formula is easy. Defining a direct complete transition function in presence of incomplete information for a general representation, other than the belief state, is particularly hard due to conditional action effects. To address this, I propose a generic abstract algorithm, called GAA, for defining such function given an arbitrary representation. Using the GAA algorithm, my doctoral thesis investigates the properties of different logical formulae and their applicability in planning under uncertainty as a belief state representation. The results obtained so far are very promissing as the research work developed several highly competitive planners which outperform other state-of-the-art planners in most benchmarks available in the literature.