This chapter investigates the following types of equations: measure functional differential equations (FDEs), impulsive FDEs, functional dynamic equations on time scales, impulsive functional dynamic equations on time scales, all of which involving Banach space-valued functions. The main advantage behind the theory of dynamic equations comes from the fact that it can unify and extend the continuous analysis. The chapter presents an example of a function whose indefinite integral satisfies a Carathéodory-type condition, showing that indeed the conditions are more general than those found in the literature for classical differential equations. It also investigates a relation between Perron Δ-integrals and Perron–Stieltjes integrals. The chapter provides averaging principles for impulsive measure FDEs and impulsive functional dynamic equations on time scales. It is devoted to results on continuous dependence on time scales of solutions of dynamic equations on time scales.