After a short review of the experimental foundations of metric theories of gravity, the choice of general relativity as a theory to be used for the routine modelling of Gaia observations is justified. General principles of relativistic modelling of astronomical observations are then sketched and compared to the corresponding Newtonian principles. The fundamental reference system - the Barycentric Celestial Reference System - which has been chosen to be the relativistic reference system underlying the future Gaia reference frame is presented. Principal relativistic effects in each constituent of a relativistic model of astronomical observations are briefly elucidated. The structure of a relativistic model of positional observations which can be used as a standard relativistic model for Gaia is sketched. The physical meaning of the Gaia reference frame is discussed. It is discussed also how Gaia observations can be used to verify general relativity.