Higher Spins in Harmonic Superspace

We review an off-shell formulation of ${\cal N}=2$ higher spin supermultiplets within the harmonic superspace approach. Each supermultiplet is encompassed by a triple of unconstrained harmonic analytic gauge superfield potentials and at the linearized level is described by a universal gauge-invariant and ${\cal N}=2$ supersymmetric action. To the first order in gauge superfields, we present their off-shell cubic couplings to ${\cal N}=2$ matter hypermultiplets and define the higher-spin gauge transformations of the latter. This new direction of applications of the harmonic superspace method is potentially rather prospective, both in the classical and quantum domains, and we discuss in brief its some nearest uses. The talk is based on two recent published works with Ioseph Buchbinder and Nikita Zaigraev (JHEP 2021, 2022) and a work in progress.