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This article presents a tutorial overview of models for estimating the quality experienced by users of speech transmission and communication services. Such models can be classified as either parametric or signal based. Signal-based models use input speech signals measured at the electrical or acoustic interfaces of the transmission channel. Parametric models, on the other hand, depend on signal and system parameters estimated during network planning or at run time. This tutorial describes the underlying principles as well as advantages and limitations of existing models. It also presents new developments, thus serving as a guide to an appropriate usage of the multitude of current and emerging speech quality models.