ESA’s space astrometry mission Gaia is expected to provide the most comprehensive and accurate catalogue of stellar positions, proper motions and parallaxes for galactic and astrophysical research in the coming decades. Accurate characterization of the errors in the catalogue is essential for making optimal use of the data. First I will shown how Gaia observes and how the observations are used to determine the astrometric parameters. Using Monte Carlo simulations I demonstrate that the astrometric errors can be decomposed in different components, and explain why the attitude component introduces correlations between the astrometric parameters of different sources. Based on this knowledge a covariance model can be derived which allows for the accurate estimation of the variances of, and correlations between, the more than one billion astrometric parameters. Finally I will shortly discuss the impact of CCD radiation damage on astrometry and present the overall conclusions from my PhD work.