We first prove in this talk the global unique solvability of the 2-D incompressible inhomogeneous Navier-Stokes equations (INS) with large initial data in the critical Besov space, which is almost the energy space in the sense that they have the same scaling in terms of this 2-D system. For the 3D INS with variable viscosity coefficient, we get its global well-posedness with the initial density in critical multiplier spaces.