Perovskite materials host an incredible variety of functionalities. Although the lightest element, hydrogen, is rarely encountered in oxide perovskite lattices, it was recently observed as the hydride anion H−, substituting for the oxide anion in ​BaTiO3. Here we present a series of 30 new complex hydride perovskite-type materials, based on the non-spherical ​tetrahydroborate anion ​BH4− and new synthesis protocols involving rare-earth elements. Photophysical, electronic and ​hydrogen storage properties are discussed, along with counterintuitive trends in structural behaviour. The electronic structure is investigated theoretically with density functional theory solid-state calculations. BH4-specific anion dynamics are introduced to perovskites, mediating mechanisms that freeze lattice instabilities and generate supercells of up to 16 × the unit cell volume in AB(BH4)3. In this view, homopolar hydridic di-hydrogen contacts arise as a potential tool with which to tailor crystal symmetries, thus merging concepts of molecular chemistry with ceramic-like host lattices. Furthermore, anion mixing ​BH4−←X− (X−=Cl−, Br−, I−) provides a link to the known ABX3 halides.