The aim of this talk is to review the current knowledge on the steady solutions of the Navier–Stokes equations in the whole two-dimensional plane. This case is more difficult than the three-dimensional space for some reasons that will be discussed. In the first part, I will discuss the construction of weak solutions through topological methods, and in the second part how the scaling invariance can be used to construct perturbative solutions. I will mainly focus on the open problems and introduce some numerical results and conjectures.