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State-of-the-art natural language processing models are anything but compact. Syntactic parsers have huge grammars, machine translation systems have huge transfer tables, and so on across a range of tasks. With such complexity come two challenges. First, how can we learn highly complex models? Second, how can we efficiently infer optimal structures within them?Hierarchical coarse-to-fine methods address both questions. Coarse-to-fine approaches exploit a sequence of models which introduce complexity gradually. At the top of the sequence is a trivial model in which learning and inference are both cheap. Each subsequent model refines the previous one, until a final, full-complexity model is reached. Because each refinement introduces only limited complexity, both learning and inference can be done in an incremental fashion. In this dissertation, we describe several coarse-to-fine systems.In the domain of syntactic parsing, complexity is in the grammar. We present a latent variable approach which begins with an X-bar grammar and learns to iteratively refine grammar categories. For example, noun phrases might be split into subcategories for subjects and objects, singular and plural, and so on. This splitting process admits an efficient incremental inference scheme which reduces parsing times by orders of magnitude. Furthermore, it produces the best parsing accuracies across an array of languages, in a fully language-general fashion.In the domain of acoustic modeling for speech recognition, complexity is needed to model the rich phonetic properties of natural languages. Starting from a mono-phone model, we learn increasingly refined models that capture phone internal structures, as well as context-dependent variations in an automatic way. Our approaches reduces error rates compared to other baseline approaches, while streamlining the learning procedure.In the domain of machine translation, complexity arises because there and too many target language word types. To manage this complexity, we translate into target language clusterings of increasing vocabulary size. This approach gives dramatic speed-ups while additionally increasing final translation quality.