The Stokes-Darcy problem has received a growing attention by the mathematical community over the last decade not only due to its many possible applications, but also to its mathematical nature. Indeed, it is a good example of a multi-physics problem where two different boundary value problems are coupled into a global heterogeneous one. To compute the approximate solution of this problem one could solve it in a monolithic way using either a direct or a suitably preconditioned iterative method. However, its multi-physics nature makes it suitable to splitting methods typical of domain decomposition techniques. These methods allow to recover the solution of the global problem by iteratively solving each subproblem separately and they permit to reuse software specifically developed to deal with either incompressible or porous media flows. The difficulty of this approach is to guarantee effective convergence and robustness of the iterations. In this talk, several domain decomposition methods for the Stokes-Darcy problems will be presented. Their robustness and performance will be analyzed and numerical examples will show their effectiveness for practical applications.