Applications of stochastic models in biological settings are discussed and reviewed in the context of first passage problems. These applications arise across a wide range of length and time scales. Within models that are effectively Markovian, we review canonical examples of first passage problems spanning applications to molecular dissociation and selfassembly, molecular search, transcription and translation, cellular mutation and disease, and organismic evolution and population dynamics. After an initial technical overview, we survey representative applications and their corresponding models. Various approximation methods and the distinction between single particle and multiple particle exit times are discussed. Finally, potentially new applications and approaches are presented. 1
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