Postdoctoral researchers are important contributors to European higher education, playing significant roles in research, but also in teaching and societal engagement. Despite their valuable contribution, the situation of postdoctoral researchers remains challenging in Europe as issues such as temporary or short-term contracts, high workloads and financial insecurity impact their work and mental health. In this context, many European universities are stepping up the support they provide at institutional level to shape highly skilled and well-rounded postdoctoral researchers, ready to explore a broad variety of job opportunities both inside and beyond academia. This report outlines the conclusions of the EUA-CDE Thematic Peer Group on "Profiles and institutional support for postdoctoral researchers", established in 2023 to provide an overview of the current services and resources available at the postdoctoral level. With findings gathered from 28 universities in 16 European countries, this publication reflects the group's discussions concerning the current state of play and the most pressing issues faced by postdoctoral researchers. This report addresses existing institutional support in place for the postdoctoral community, discusses new strategies, provides examples of good practices and suggests possible ways forward for European universities on how to improve the postdoctoral experience. It also serves as a source of reflection for institutions considering creating a more sustainable environment for this population and fostering their postdoctoral services and support.