Since the breakthrough proof-of-concept Mg metal - Chevrel Mo6S8 battery, the promise of multivalent batteries has been limited by the lack of higher energy density cathodes with high intercalant mobility and matching high-voltage electrolytes. In this talk we will describe our recent collaborative work within the Joint Center of Energy Storage Research on unraveling the design rules behind multivalent mobility. We will describe how the host structure and chemistry needs to be carefully tuned to the electronic structure and preferred coordination environment of the mobile cation in order to enable facile intercalation. The preferences of Zn, Ca and Mg will be particularly highlighted; in comparison with Li. Recent experimental progress on Zn as well as Mg cathodes will be discussed in light of the theoretical understanding and predictions.