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) x SU(2) harmonic superspace and (ii) the harmonic superspace formulation of ”small”N = 4 SU(2) superconformal algebra and the related super KdV hierarchy.