The first-passage time is a key quantity for evaluating the kinetics of various processes, and in particular chemical reactions involving "small" numbers of particles. A striking example is given by gene transcription, where specific proteins search for target sequences on DNA.
I will present asymptotic results which enable the evaluation of the  first-passage time statistics to a target site for a wide range of random processes  in  confined domains, and show how these results can be extended to non Markovian processes, which are often needed to model transport in complex environments.