The aim of this talk is to review the current knowledge on the stationary solutions of the Navier–Stokes equations in the whole space $\mathbb{R}^3$ and mainly in the whole plane $\mathbb{R}^2$. Contrary to the Cauchy problem for which the $\mathbb{R}^3$ domain is more complicated than $\mathbb{R}^2$, for the stationary problem, this is the opposite: $\mathbb{R}^2$ is the most difficult case. In the first part, I will discuss the construction of weak solutions by topological methods, and in the second part, I will show how scale invariance can be used to construct perturbative solutions. Open problems will be discussed and I will also present some numerical results and conjectures. Joint work with Mikhail Korobkov, Xiao Ren, and Peter Wittwer.