A general formalism is presented to describe recurrences and recurrence-time distributions in coarse-grained classical dynamical systems in discrete time. The connections between exit time, escape time and recurrence time distributions are deduced. The formalism is then applied to progressively more complex dynamical behaviour, starting with multiply periodic systems and progressing through quasi periodic, chaotic and intermittently chaotic dynamics. The case of continuous-time dynamics is then considered. Finally, if time permits, some work on the analogues of recurrences in quantum dynamics will be described.