In addition to traditional, cluster-oriented approaches, both cross-sectional technologies ("key enabling technologies") and societal challenges ("grand challenges") are becoming increasingly important for regional innovation strategies. A more complex, multi-dimensional approach of regional innovation strategies requires but a number of adaptations, which need to adjust to various, different regional preconditions. The article raises the research question how societal demands are considered and implemented by regional innovation strategies in four case study regions: Pirkanmaa/Tampere region in Finland, Groningen region in the Netherlands, West Flanders in Belgium, and the Federal State of Bremen in Germany. The four regional case studies are comparable European regions in terms of their innovation capacity and their level of innovation (all are classified "highly innovative" or "strong innovator" by the European Union). In order to address global societal goals and challenges - in particular climate change and its consequences as well as demographic change - a multidimensional innovation policy spanning sectors and technologies and a close interlinking of technological and societal innovation objectives and strategies, seems inevitable. The analyses revealed that governance structures and the innovation infrastructures in the regions indeed start to adapt to societal needs and to the increasing complexity of regional innovation strategies, though the speed as well as the intensity of transition and adjustment varies greatly across the regions. Interregional learning as is intended by the European Interreg programme could offer meaningful support for the progress of regional measures towards multi-dimensional innovation policies.