Let $f : P^1_K \to P^1_K$ be a rational map defined over a number field $K$. The Galois theory of the iterates $f_n = f \circ . . . \circ f$ has applications both in number theory and arithmetic dynamics. In this talk, we will discuss the various Galois groups attached to the iterates of f, namely arithmetic and geometric monodromy groups and Arboreal Galois representations. While providing a survey of recent results on the subject, we will also talk about joint work with I. Bouw and V. Karemaker on Dynamical Belyi maps.