Halogen fluorides are textbook examples of how fundamental chemical concepts, such as molecular orbital theory or the valence-shell electron-repulsion (VSEPR) model, can be used to understand the geometry and properties of compounds. However, it is still an open question whether these notions are applicable to matter subject to high pressure (>1 GPa). In an attempt to gain insight into this phenomenon, we present a computational study on the phase transitions and reactivity of bromine fluorides at pressures of up to 100 GPa (≈106 atm). We predict that at a moderately high pressure of 15 GPa, the bonding preference in the Br/F system should change considerably with BrF3 becoming thermodynamically unstable and two novel compounds emerging as stable species: BrF2 and BrF6. Calculations indicate that both these compounds contain radical molecules while being non-metallic. We propose a synthetic route for obtaining BrF2 which does not require the use of highly reactive elemental fluorine. Finally, we show how molecular orbital diagrams and the VSEPR model can be used to explain the properties of compressed bromine fluorides.