In 2001, Whyte proved that all 'higher' Baumslag–Solitar groups, i.e. BS(p,q), with |p|,|q|≠1 and |p|≠|q|, are quasi-isometric, thereby completing the quasi-isometry classification of all Baumslag–Solitar groups initiated by Farb and Mosher. Since then, the question of their measure equivalence has remained an intriguing open problem. In joint work with D. Gaboriau, A. Poulin, R. Tucker-Drob, and K. Wrobel, we solve this problem, establishing the measure equivalence analogue of Whyte's theorem. We do so by first reducing the problem to the measure equivalence of the automorphism groups of the Basse–Serre trees of the higher Baumslag–Solitar groups, which are nonunimodular locally compact groups. This shift from unimodular (discrete) to nonunimodular groups naturally changes the setting from probability-measure-preserving to merely measure-class-preserving, where recent advances in descriptive set theory and some new ideas are leveraged.