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We introduce and characterize slant Riemannian submersions from Sasakian manifolds onto Riemannian manifolds. We survey main results of slant Riemannian submersions defined on Sasakian manifolds. We give a sufficient condition for a slant Riemannian submersion from Sasakian manifolds onto Riemannian manifolds to be harmonic. We also give an example of such slant submersions. Moreover, we find a sharp inequality between the scalar curvature and norm squared mean curvature of fibres.