The Shimura-Waldspurger correspondence for Mp(2n)

We describe some recent developments and formulate some conjectures in the genuine representation theory and the study of automorphic forms of the metaplectic group $\mathrm{M}\mathrm{p}(2n)$, from the point of view of the theta correspondence as well as from the point of view of the theory of endoscopy and the trace formula.