The scope of solid-state transitions, from melting temperatures down to 4.2 K, is described for six systems: K x VF 3 , Rb x VF 3 , Cs x VF 3 , K x CrF 3 , Rb x CrF 3 , and Cs x CrF 3 (for x = 0.0 to 1.0). Connections are drawn between the compounds' compositions and structures with the various transitions and ordering events. Upon solidification from the melt and gradual cooling to room temperature, a sequential descent of symmetry appears to occur, from high-symmetry perovskite phases, through possible reconstructive transitions, to phases designated α, β, and δ, within which ionic ordering finally sets in, forming many new lower-symmetry structures. Many stable new structures are seen at room temperature. Finally, at cryogenic temperatures, magnetic ordering sets in. Other anomalies for these systems are also described. The analysis underscores the overall correspondence of structure, composition, and magnetic properties in these compounds. This lowering of symmetry mirrors what has been chronicled for oxygen-bearing perovskites that have yielded so many high-temperature ceramic superconductors.