This talk is about joint work with Ralf Schmidt, and follows his talk on local newforms for $GSp(4)$ (in the representation theory seminar on Tues, Feb 1st). In this talk we will discuss a conjecture which describes a theory of Siegel modular newforms of degree two with respect to the paramodular group. Using our local theory, we will indicate how this conjecture follows from a corresponding conjecture in the language of automorphic representations. Finally, we will discuss how the corresponding conjecture is implied by the conjectural detailed structure of the discrete spectrum of $GSp(4)$.