In this talk, we will introduce some progress of Domain Decomposition methods for the coupled Stokes-Darcy model. One is the fully mixed parallel domain decomposition method, with the newly constructed Robin-type boundary conditions, the present method adopts modified weak formulation to decouple the original problem into two independent subproblems. The equivalence between the original problem and the decoupled subproblems is derived under some compatibility conditions. With some suitable choice of parameters, both mesh-dependent and mesh-independent convergence rates are proved rigorously. The other are two-grid Robin-type domain decomposition methods, which firstly adopt the existing Robin-type domain decomposition algorithm to obtain the coarse grid approximate solutions. Then the modified domain decomposition methods are further constructed on the fine grid by utilizing the framework of two-grid methods to enhance computational efficiency, via replacing some interface terms by the coarse grid information.