The hydrophobicity of CeO2 surfaces is examined here. Since wettability measurements are extremely sensitive to experimental conditions, we propose a general approach to obtain contact angles between water and ceria surfaces of specified orientations based on density functional calculations. In particular, we analysed the low index surfaces of this oxide to establish their interactions with water. According to our calculations, the CeO2 (111) surface was the most hydrophobic with a contact angle of {Theta} = 112.53{deg} followed by (100) with {Theta} = 93.91{deg}. The CeO2 (110) surface was, on the other hand, mildly hydrophilic with {Theta} = 64.09{deg}. By combining our calculations with an atomistic thermodynamic approach, we found that the O terminated (100) surface was unstable unless fully covered by molecularly adsorbed water. We also identified a strong attractive interaction between the hydrogen atoms in water molecules and surface oxygen, which gives rise to the hydrophilic behaviour of (110) surfaces. Interestingly, the adsorption of water molecules on the lower-energy (111) surface stabilises oxygen vacancies, which are expected to enhance the catalytic activity of this plane. The findings here shed light on the origin of the intrinsic wettability of rare earth oxides in general and CeO2 surfaces in particular and also explain why CeO2 (100) surface properties are so critically dependant on applied synthesis methods.