The structural and thermodynamic properties of MgF2 have been investigated in a wide range of pressures (0-80 GPa) and temperatures (0-850 K) by coupling quantum-mechanical ab initio perturbed ion calculations with a quasi-harmonic Debye model. The room temperature, zero-pressure structural parameters and lattice energy are computed with errors smaller than 2% when correlation energy corrections are incorporated in the calculation. Our computed equation of state is compatible with direct measurements of the bulk modulus and obeys universal p-V relations. We have simulated the rutile-to fluorite phase transition during the loading process and have found lower (similar or equal to 4 GPa) and upper (similar or equal to 45 GPa) bounds for the transition pressure by means of thermodynamic and mechanical criteria for phase stability. Bonding properties and their change with pressure have been derived through a topological analysis of the electron density using Bader＇s theory of atoms in molecules. This analysis reveals that MgF2 is a highly ionic compound. Its ionicity decreases linearly with increasing pressure and, as in other ionic compounds, the crystal shows anion-anion bonds.