  We discuss recent progress in describing a certain non-Abelian vortex string
as a critical superstring on a conifold and clarify some subtle points. This
particular solitonic vortex is supported in four-dimensional N=2 supersymmetric
QCD with the U(2) gauge group, N_f=4 quark flavors and the Fayet-Iliopoulos
term. Under certain conditions the non-Abelian vortex can become infinitely
thin and can be interpreted as a critical ten-dimensional superstring. In
addition to four translational moduli the non-Abelian vortex under
consideration carries six orientational and size moduli. The vortex moduli
dynamics are described by a two-dimensional sigma model with the target space
{R}^4\times Y_6 where Y_6 is a non-compact Calabi-Yau conifold. The closed
string states which emerge in four dimensions (4D) are identified with hadrons
of 4D bulk N=2 QCD. It turns out that most of the states arising from the
ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical
massless hypermultiplet associated with the deformation of the complex
structure of the conifold is found. It is interpreted as a monopole-monopole
baryon of the 4D theory (at strong coupling).
