This paper assesses the origins, evolution and prospects of national innovation systems (NISs) using bibliometric techniques. All available data in the Web of Science Core Collection database up to and including the year 2017 are considered in the analysis. Both the number of NIS studies and the number of citations of these studies reflect the influence of this topic and the attention and growing interest of the scientific community, public administrations and international organisations in NIS research. The co-citation analysis of cited references provides a historical view of the origins of the NIS, and the bibliographic coupling between the documents gives a current overview of the status of NIS research. Our approach highlights the fact that many studies belong to previous, well-developed research streams. We also examine the topics covered by recent studies in each stream and the evolution of the most common keywords over time. In conclusion, we propose a research agenda based on three pillars: (1) the adaptation of innovation systems to the current global economic crisis and the application of the Quintuple Helix model to deal with this new scenario, (2) the adaptation of innovation systems to developing countries and (3) the specific fit of entrepreneurship and entrepreneurial innovations into NIS research.