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Summary form only given. Traditionally, "language" models capture only the word sequences of a language. A crucial component of spoken language, however is its prosody, i.e., rhythmic and melodic properties. This paper summarizes recent work on integrated, computationally efficient modeling of word sequences and prosodic properties of speech, for a variety of speech recognition and understanding tasks, such as dialog act tagging, disfluency detection, and segmentation into sentences and topics. In each case it turns out that hidden Markov representations of the underlying structures and associated observations arise naturally, and allow existing speech recognizers to be combined with separately trained prosodic classifiers. The same HMM-based models can be used in two modes: to recover hidden structure (such as sentence boundaries), or to evaluate speech recognition hypotheses, thereby integrating prosody into the recognition process.