Higher Spins in Harmonic Superspace

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