We study Yang–Baxter deformations of 4D Minkowski spacetime. We obtain metrics and $B$–fields as Yang–Baxter deformations which correspond to well-known configurations such as T–duals of Melvin backgrounds, Hashimoto–Sethi and Spradlin–Takayanagi–Volovich backgrounds, the T–dual of Grant space, pp-waves, and T–duals of $dS_4$ and $AdS_4$. Finally we consider a deformation with a classical $r$-matrix of Drinfeld–Jimbo type and explicitly derive the associated metric and $B$–field which we conjecture to correspond to a new integrable system.