Higher spins in harmonic superspace

We report on a recent progress in constructing off-shell $4$D, $\mathcal{N}=2$ supersymmetric integer higher-superspin theory in terms of unconstrained harmonic analytic gauge superfields and their cubic interaction with matter hypermultiplets. For even superspins, a new equivalent representation of the hypermultiplet couplings in terms of an analytic $\omega$ superfield is presented. It involves both cubic and quartic vertices.