  Applications of first passage times in stochastic processes arise across a
wide range of length and time scales in biological settings. After an initial
technical overview, we survey representative applications and their
corresponding models. Within models that are effectively Markovian, we discuss
canonical examples of first passage problems spanning applications to molecular
dissociation and self-assembly, molecular search, transcription and
translation, neuronal spiking, cellular mutation and disease, and organismic
evolution and population dynamics. In this last application, a simple model for
stem-cell ageing is presented and some results derived. Various approximation
methods and the physical and mathematical subtleties that arise in the chosen
applications are also discussed.
