Unconstrained $\mathcal{N}=2$ higher-spin gauge superfields and their hypermultiplet couplings

In recent papers arXiv:2109.07639 [hep-th] and arXiv:2202.08196 [hep-th], we constructed free off-shell $\mathcal{N}=2$ supersymmetric higher spin gauge theories in harmonic superspace and their cubic couplings to hypermultiplet. The present report is a brief review of the results obtained.