Extended keynote paper of Eurosteel 2021. This article provides an overview of the various support structures for offshore wind turbines and addresses the challenges that arise for the different design variants. First of all, the existing types of support structures are explained and their benefits and shortcomings discussed. Following that, the focus is on material fatigue and its analysis, which is of great importance due to the cyclic loading on the structures. A central topic of this article is the experimental evaluation of fatigue strength using large-scale test setups and state-of-the-art measurement methods. Critical and complex design details such as welds for extremely thick plates, tubular joints, grouted connections, large HV bolts and ring flanges are investigated to improve methods of analysis. Further, the new series of German standards (DIN 18088) for support structures for wind energy turbines and platforms is addressed. Finally, these topics are summarized and the importance of offshore wind energy for the transition to cleaner energy is emphasized.