This talk will describe the use of weighted transducers in speech and language processing. Weighted transducers are automata where each transition has an input label, an output label, and a weight. They have key applications in speech recognition and synthesis, machine translation, optical character recognition, pattern matching, string processing, machine learning, information extraction and retrieval among others. We give a brief history of the field, an overview of the theory and algorithms of weighted finite-state and pushdown transducers, a discussion of available software libraries, and a description of applications to speech recognition, speech synthesis, machine translation and NLP.