  A brief review of the harmonic superspace approach to the construction of
$\mathcal{N}=2$ supersymmetric higher spin theories is given. We define
off-shell analytic harmonic gauge potentials of $\mathcal{N}=2$ supersymmetric
higher-spin multiplets and of $\mathcal{N}=2$ superconformal higher-spin
multiplets for an arbitrary integer highest spin. The component contents of
these $\mathcal{N}=2$ higher-spin supermultiplets are explicitly presented. We
also construct their cubic couplings to the hypermultiplet. This short report
summarizes the basic results of the series of published papers [1-3] as well as
announces those of the forthcoming article [4].
