Classical planning is the problem of finding a sequence of actions for achieving a goal from an initial state assuming that actions have deterministic effects. The most effective approach for finding such plans is based on heuristic search guided by heuristics extracted automatically from the problem representation. In this thesis, we introduce alternative approaches for performing inference over the structure of planning problems that do not appeal to heuristic functions, nor to reductions to other formalisms such as SAT or CSP. We show that many of the standard benchmark domains can be solved with almost no search or a polynomially bounded amount of search, once the structure of planning problems is taken into account. In certain cases we can characterize this structure in terms of a novel width parameter for classical planning.