A combined experimental-theoretical study of silver(I) and silver(II) fluorides under high pressure is reported. For AgI, the CsCl-type structure is stable to at least 39 GPa; the overtone of the IR-active mode is seen in the Raman spectrum. Its AgIIF2 sibling is a unique compound in many ways: it is more covalent than other known difluorides, crystallizes in a layered structure, and is enormously reactive. Using X-ray diffraction and guided by theoretical calculations (density functional theory), we have been able to elucidate crystal structures of high-pressure polymorphs of AgF2. The transition from ambient pressure to an unprecedented nanotubular structure takes place via an intermediate orthorhombic layered structure, which lacks an inversion center. The observed phase transitions are discussed within the broader framework of the fluorite → cotunnite → Ni2In series, which has been seen for other metal difluorides.