A family of double perovskites comprises a very broad range of compounds, displaying a variety of properties and raising interest from physicists, chemists and applied scientists. In this talk I will focus on our recent work on 5d1 compounds, with an emphasis on Ba2MgReO6. Here, the magnetism arises from a single electron occupying t2g orbitals under the influence of strong spin-orbit coupling, resulting in the ground state quartet. Thermodynamic measurements reveal two features, and from resonant x-ray scattering (REXS) it is possible to associate them with long-range order of magnetic dipoles developing below 18 K and charge quadrupoles below 31 K. On the other hand, careful specific heat studies reveal that in the range 2 - 50 K recovered entropy reaches only Rln2, indicating a doublet as a ground state. Contrary to the predominant view, we show evidence of a persisting doublet-doublet gap revealed by resonant inelastic x-ray scattering (RIXS). The puzzle of the ground-state degeneracy and its relation to the observed quadrupolar order can be resolved by invoking a dynamical Jahn-Teller distortion of ReO6 octahedra, unscathed by both transitions, and eventually freezing out only below 1 K. This implies a novel environment for magnetic dipoles and charge quadrupoles, in which their interaction through intermediate oxygen ions is strongly renormalized due to a varying p-p orbital overlap. Our results will have a direct impact onto the understanding of double perovskite compounds in which strong covalent bonds with ligands are formed on a single site.