Ideas from model theory, especially around the theory ACFA of existentially closed difference fields, have direct interpretations in and applications to the theory of algebraic dynamical systems.

In this tutorial, I will explain a dictionary between definability in difference fields and corresponding concepts in algebraic dynamics and then expose three specific connections: (1) a structure theory for definable sets in ACFA and for algebraic dynamical systems, (2) the relation between the theory of canonical bases and descent in algebraic dynamics, and (3) the use of o-minimality and the model theory of valued fields in dynamical Mordell-Lang-type problems.