I present a method to expand in components four dimensional superconformal multiplets in N=1 and N=2 superconformal field theories. The method consists in constructing a differential operator for each descendant, which can then be applied on any correlator in superspace. In particular I show how the action on three-point functions can be considerably simplified. An interesting application of the formalism is the proof that N=2 spinning chiral primaries (also called ‘exotic’ primaries) cannot exist in any local SCFT. The interest in constraining this particular kind of operator stemmed from a result in the literature that ruled them out from a very large class of theories. I also discuss the role of the differential operators in the computation of superconformal blocks.