This thesis is devoted to the study of the incompressible and stationary Navier-Stokes equations in two-dimensional unbounded domains and in particular when the velocity field at infinity is zero. After a review concerning the weak solutions, strong solutions are constructed under some hypothesis by using the properties of the linearized equations, however it is shown that in general the solutions of the linear and nonlinear equations cannot have the same asymptotic behavior. A nonperturbative asymptotic expansion of the solutions that produce a nonzero net force is proposed and numerically validated. For a zero net force, exact solutions are constructed and the general asymptotic behavior is studied formally and numerically. Afterward, the asymptote of the vorticity valid in all directions is determined when the velocity at infinity is a nonzero constant. Finally, the Navier-Stokes equations are studied in the half-plane with a flux through the boundary.