Symmetric and nonsymmetric Macdonald polynomials associated to root systems are very general families of orthogonal polynomials in multiple variables. Their definition is quite complex, but in certain cases one can define so-called interpolation polynomials that have a surprisingly simple definition and are related to the Macdonald polynomials by a binomial formula. In this thesis we will discuss such formulas for two kinds of root systems: type A and type (C^∨,C). For the latter case, there are still some open questions that remain unanswered.