Any self-map \(f\) of projective space can be written in terms of homogeneous polynomials of some degree, the ``algebraic degree” of the map \(f\). What is the algebraic degree of the \(n\)-th iterate \(f^n\)? If \(f\) is a rational map, this question has a subtle answer, leading us to a key invariant of a dynamical system, its dynamical degree. This talk is a gentle introduction to dynamical degrees, building up the handful of facts from algebraic geometry that we need to define them.