$N=2$ supersymmetric higher-spin theory in harmonic superspace

We consider new results obtained using harmonic superspace in higher spin theories with extended $N=2$ supersymmetry. The superfield formulation of the $N=2$ supersymmetric theory of higher spins, its cubic interaction with the hypermultiplet, and the superfield currents of the hypermultiplet corresponding to the higher spin symmetries will be presented. The obtained results will then be extended to the superconformal $N=2$ theory of higher spins, in which a number of remarkable properties appear, the most striking of which is the fully consistent interaction vertex of hypermultiplet with an infinite tower of higher spins on an arbitrary background of conformal supergravity.