This chapter describes a general representation and algorithmic framework for speech speechrecognition recognition based on weighted finite-state weighted transducer transducers. These transducers provide a common and natural representation for major components of speech recognition systems, including hidden Markov models (HMMs), context-dependency models, pronunciation dictionaries, statistical grammars, and word or phone lattices. General algorithms for building and optimizing transducer models are presented, including composition for combining models, weighted determinization and minimization for optimizing time and space requirements, and a weight pushing algorithm for redistributing transition weights optimally for speech recognition. The application of these methods to large-vocabulary recognition tasks is explained in detail, and experimental results are given, in particular for the North American Business News (NAB) task, in which these methods were used to combine HMMs, full cross-word triphones, a lexicon of 40000 words, and a large trigram grammar into a single weighted transducer that is only somewhat larger than the trigram word grammar and that runs NAB in real time on a very simple decoder. Another example demonstrates that the same methods can be used to optimize lattices for second-pass recognition.