The European XFEL comprises three undulator systems. All of the systems use standardized mechanical, magnetic and control components. The key elements such as undulators, phase shifters and quadrupole movers as well as their controls are described, with special emphasis on the SASE1 undulator system, which was the first to become operational and has been lasing since May 2017. The role of these systems for the commissioning is outlined with special emphasis on beam-based alignment, which was important to achieve first lasing. Radiation damage was observed. The exposure doses were measured with the online radiation dosimetry system. Countermeasures and latest results are reported, which are important for a high-duty-cycle machine such as the European XFEL.