In 1987, S. Kobayashi remarked the following interesting similarity between CR-submanifolds of Kähler manifolds and Riemannian submersions: both concepts imply the existence of two distributions, one of which is always integrable Kobayashi, S. Using this similarity, the author introduced the notion of CR-submersion as a Riemannian submersion \(\pi :M\rightarrow B\) with total space a CR-submanifold M of a Kähler manifold \((\bar {M},J,\bar {g})\) and base space an almost Hermitian manifold \((B,J',g')\) such that the horizontal distribution \(\mathcal {H}\) of \(\pi \) is nothing but the holomorphic distribution \(\mathcal {D}\) of the CR-submanifold M, the vertical distributions \(\mathcal {V}\) of \(\pi \) is precisely the totally real distribution of M, while \(\pi \) restricted to \(\mathcal {D}\) is a complex isometry.