A subset of the positive integers is dynamically central syndetic if it contains the times of return of a point to a neighborhood of itself in a minimal dynamical system. This class of syndetic sets forms an important bridge between dynamics and combinatorics. We show that a set is dynamically central syndetic if and only if it is a member of a syndetic, idempotent filter. We elaborate on the consequences of this characterization for the dual family: sets of pointwise recurrence. For example, we provide several combinatorial characterizations of sets of pointwise recurrence, show that these sets do not have the Ramsey property, and they are sets of multiple recurrence. These results answer several questions asked by Host, Kra, and Maass. This talk is based on an joint work with Daniel Glasscock (University of Massachusetts Lowell).