The catalytic fluorination of hydrocarbons facilitates the large-scale production of chlorofluorocarbons for a wide range of applications including aerosol propellants, refrigerants and solvents. Lewis acid catalysts, such as Swarts catalysts based on antimony pentafluoride, are commonly used. Recently, a sol-gel based synthesis method has been developed which yields very high surface area aluminium fluoride (HS-AlF3) that has a Lewis acidity comparable to that of the Swarts catalysts. This makes HS-AlF3 a promising candidate for use in several Lewis acid catalysed reactions. Despite the importance of the surface in the catalytic process little is known about the detailed atomic scale structure of AlF3 surfaces. Surface thermodynamics calculations, based on hybrid-exchange density functional theory, are employed to predict the composition and structure of AlF3 surfaces. The surfaces of AlF3 expose under coordinated Al ions that are potential Lewis acid sites. Under standard atmospheric conditions the AlF3 surfaces are shown to adsorb water above the under coordinated Al ions. Theoretical characterisation of the under coordinated Al ions shows that the most reactive type of site is not exposed on crystalline α-AlF3 samples, however, it is predicted to occur in small quantities on β crystallites. It is speculated that such sites occur in higher quantities on the high surface area materials. This result may explain the different reactivity of α-, β- and HS-AlF3. Our detailed understanding of AlF3 surfaces allows us to propose a reaction centre and mechanism for the dismutation of CCl2F2 on β-AlF3. Aluminium chloride is extensively used as a catalyst in Friedal-Crafts reactions. It is therefore, commonly assumed that pure crystalline AlCl3 is strongly Lewis acidic. Ab initio surface thermodynamics calculations are used to study the surfaces of crystalline AlCl3 and show that it is chemically inert.