Magnetoelectric (ME) multiferroic materials, which present simultaneously two coupled properties between ferromagnetism and ferroelectricity, have attracted much attention recently, not only owing to their application perspectives, e.g., next-generation magnetic RAM, but also for the rich physics associated with the understanding of this coupling. Inverse trirutiles are of particular interest here since ME properties have been reported in this family of compounds. This manuscript presents the study of inverse trirutile Mn2TeO6 and its Cr-substitution series Mn2-xCrxTeO6. Mn2TeO6 and Cr-substituted series were prepared by solid state reaction at relatively low-temperature (< 700°C). Thanks to an extensive use of different techniques performed in a large temperature range (1.5K to 700°C), encompassing synchrotron, neutron and electron diffraction experiments combined with physical properties measurements, the very complex behaviour of Mn2TeO6 was revealed. A structural transition at 400°C from tetragonal (P42/mnm) to monoclinic (P21/c) is observed first, and related to a cooperative Jahn-Teller effect. Further cooling the sample, a hysteretic structural transition is observed spanning more than 50K, which leads to the coexistence of two monoclinic phases. A series of magnetic transitions are also observed between 48K and 22K, with magnetization, heat capacity measurement and neutron diffraction. Cr-substituted (x ≥ 0.15) samples crystallize in the tetragonal phase, implying the suppression of the cooperative Jahn-Teller effect, and involving a simpler, though short–range, magnetic order.