Euclid, an ESA mission designed to characterise dark energy and dark matter, passed its Mission Critical Design Review in November 2018. It was demonstrated that the project is ready to start integration and test of the main systems, and that it has the ability to fulfil its top-level mission requirements. In addition, based on the performances at M-CDR, the scientific community has verified that the science requirements can be achieved for the Weak Lensing and Galaxy Clustering dark energy probes, namely a dark energy Figure of Merit of 400 and a 2% accuracy in the growth factor exponent gamma. We present the status of the main elements of the Euclid mission in the light of the demanding high optical performance which is the essential design driver is the to meet the scientific requirements. We include the space segment comprising of a service module and payload module hosting the telescope and its two scientific instruments, and the ground segment, which encompasses the operational and science ground segment. The elements for the scientific success of the mission for a timely release of the data are shortly presented: the processing and calibration of the data, and the design of the sky survey. Euclid is presently on schedule for a launch in September 2022.