We investigate the high-pressure behaviour of beryllium, magnesium and calcium difluorides using ab initio random structure searching and density functional theory (DFT) calculations, over the pressure range 0−70 GPa. Beryllium fluoride exhibits extensive polymorphism at low pressures, and we find two new phases for this compound − the silica moganite and CaCl2 structures − which are stable over the wide pressure range 12−57 GPa. For magnesium fluoride, our searching results show that the orthorhombic 'O-I' TiO2 structure (P bca, Z = 8) is stable for this compound between 40 and 44 GPa. Our searches find no new phases at the static-lattice level for calcium difluoride between 0 and 70 GPa; however, a phase with P 62m symmetry is close to stability over this pressure range, and our calculations predict that this phase is stabilised at high temperature. The P 62m structure exhibits an unstable phonon mode at large volumes which may signal a transition to a superionic state at high temperatures. The Group-II difluorides are isoelectronic to a number of other AB2-type compounds such as SiO2 and TiO2, and we discuss our results in light of these similarities.