In this paper, we study the geometry of anti-invariant Riemanniansubmersions from a Kähler manifold onto a Riemannian manifold. Wefirst determine the base space when the total space of ananti-invariant Riemannian submersion is Einstein and then weinvestigate new conditions for anti-invariant Riemannian submersionsto be Clairaut submersions. We also focus on the geometry of Clairaut anti-invariant submersions.