Despite the seminal work of Jean Leray, the stationary Navier-Stokes equations in two-dimensional unbounded domains are still not completely understood mathematically. More precisely, the behavior at infinity of the weak solutions is an open question. The Stokes paradox states that the linearization of the Navier-Stokes equations have no bounded solutions in general. In this talk, I will explain how the nonlinearity helps to obtain bounded solutions going to zero at infinity as well as their asymptotic behavior for the full nonlinear equations.