In this talk, I shall first survey the global existence and uniqueness of solution to 3-D anisotropic Navier-Stokes equations (ANS) with initial data being small in the critical spaces; then I shall present our result on the global small analytic solutions of the system (ANS); Finally I shall present our recent result concerning the continuous and yet not uniform continuous of the solutions to this sysem with respect to the initial data in the subcritical anisotropic Sobolev spaces.
