We first introduce hemi-slant Riemannian maps and study such Riemannian maps from Kahler manifolds onto Riemannian manifolds. We give necessary and sufficient conditions for the integrability of the distributions which are involved in the definition of the Riemannian map and investigate their leaves. We also obtain harmonicity and totally geodesic conditions for such maps. Then we introduce hemi-slant Riemannian maps from arbitrary Riemannian manifolds to Kahler manifolds and find a decomposition theorem for the image. We also provide examples for both cases.