Alkali halides MX, have been viewed as typical ionic compounds, characterized by 1:1 ratio necessary for charge balance between M+ and X-. It was proposed that group I elements like Cs can be oxidized further under high pressure. Here we perform a comprehensive study for the CsF-F system at pressures up to 100 GPa, and find extremely versatile chemistry. A series of CsFn (n >= 1) compounds are predicted to be stable already at ambient pressure. Under pressure, 5p electrons of Cs atoms become active, with growing tendency to form Cs (III) and (V) valence states at fluorine-rich conditions. Although Cs (II) and (IV) are not energetically favoured, the interplay between two mechanisms (polyfluoride anions and polyvalent Cs cations) allows CsF2 and CsF4 compounds to be stable under pressure. The estimated defluorination temperatures of CsFn (n = 2,3,5) compounds at atmospheric pressure (218°C, 150°C, -15°C, respectively), are attractive for fluorine storage applications.