%0 Journal Article %T Harmonic Superspace: Some New Trends %A Evgeny A. Ivanov %J Physics %D 1996 %I arXiv %X We give a brief account of two recent applications of the harmonic superspace method: (i) an off-shell description of torsionful $(4,4)$ supersymmetric $2D$ sigma models in the framework of $SU(2)\times SU(2)$ harmonic superspace and (ii) the harmonic superspace formulation of ``small'' $N=4$ $SU(2)$ superconformal algebra and the related super KdV hierarchy. %U http://arxiv.org/abs/hep-th/9602079v1