Since their first inception more than half a century ago, automatic reading systems have evolved substantially, thereby showing impressive performance on machine-printed text. The recognition of handwriting can, however, still be considered an open research problem due to its substantial variation in appearance. With the introduction of Markovian models to the field, a promising modeling and recognition paradigm was established for automatic offline handwriting recognition. However, so far, no standard procedures for building Markov-model-based recognizers could be established though trends toward unified approaches can be identified. It is therefore the goal of this survey to provide a comprehensive overview of the application of Markov models in the research field of offline handwriting recognition, covering both the widely used hidden Markov models and the less complex Markov-chain or n-gram models. First, we will introduce the typical architecture of a Markov-model-based offline handwriting recognition system and make the reader familiar with the essential theoretical concepts behind Markovian models. Then, we will give a thorough review of the solutions proposed in the literature for the open problems how to apply Markov-model-based approaches to automatic offline handwriting recognition.