Overview of the comparative astrometric analyses of Euclid and Gaia presented by L24. The left panel shows the Gaia-G magnitude as a function of the 1D PM error (the sum in quadrature of the PM errors along the α cos δ and δ directions divided by $\sqrt{2}$). Stars present in both the Gaia DR3 and Euclid-Gaia catalogues are shown in black and red, respectively, while blue points are sources with a PM measurement only in the Euclid-Gaia catalogue (i.e. with positions but no motions available in the Gaia DR3 catalogues). The vector-point diagrams of the PMs in four magnitude bins (the thresholds of which are drawn in the left panel) are shown in the middle and right panels for the Euclid-Gaia and Gaia DR3 cases, respectively. Clearly Euclid-Gaia DR3 PMs are ten times more precise in this common magnitude interval, and provide PMs for sources with positions entries in Gaia DR3, but not PMs. However, the significant improvements over DR3 seen in the narrow magnitude range 19 < G < 21 are expected to become progressively smaller with the advent of the upcoming DR4 and DR5 of far superior astrometric precision and accuracy (see text).