Arithmetic dynamics is the study of dynamical systems from a viewpoint derived from the classical theory of Diophantine equations and arithmetic geometry. I will explain this correspondence and describe some of the main results and conjectures in the area, in particular those related to rationality of periodic points and integrality of wandering points. Additional topics, as time permits, will include dynamical canonical heights, dynamical analogues of theorems of Faltings and Raynaud, reduction modulo p, and dynamical analogues of cyclotomic fields and cyclotomic units.