The dynamic behavior of polynomials within the framework of the Fatou-Julia dichotomy is among the most fascinating topics of complex analysis. An introduction to the theory is the content of the last section of this chapter. The essential theoretical foundation is formed by the spherical normality theorem of Montel, also briefly referred to as Montel’s great theorem. As a further consequence of Montel’s great theorem, one obtains Picard’s great theorem, which in turn is undoubtedly one of the jewels of function theory.