  Often sharp changes in cellular behavior are triggered by thresholded events,
i.e., by the attainment of a threshold value of a relevant cellular or
molecular dynamical variable. Since the governing variable itself typically
undergoes noisy or stochastic dynamics, there is a corresponding variability in
the times when the same change occurs in each cell of a population. This time
is called the "first passage" time and the corresponding process is a "first
passage" (FP) process, referring to the event when a random variable first
passes the threshold value. In this review we first present and elucidate
fundamentals of the FP formalism within a unified conceptual framework, which
naturally integrates the existing techniques. We then discuss applications
thereof, with emphasis on the practical use of FP techniques in biophysical
systems. Our focus here is on covering a diverse set of analytical techniques;
the number of reviewed biological applications is thus limited, out of
necessity. We focus on three specific areas: channel transport; receptor
binding and adhesion; and single-cell growth and division.
