With the field of innovation studies now half a century old, the occasion has been marked by several studies looking back to identify the main advances made over its lifetime. Starting from a list of 20 advances over the field's history, this discussion paper sets out 20 challenges for coming decades. At a conference in 1900, David Hilbert put forward a list of 23 unsolved mathematical problems that were to have a profound influence on the work of mathematicians during the 20 th Century. The intention here is to prompt a debate within the innovation studies community on what are, or should be, the key challenges for us to take up, and more generally on what sort of field we aspire to be. It is argued that the empirical focus of our studies has not kept pace with the fast changing world and economy, especially the shift from manufacturing to services and the growing need for sustainability. Moreover, the very way we conceptualise, define, operationalise and analyse 'innovation' seems rooted in the past, leaving us less able to grapple with other less visible or 'dark' forms of innovation.Keywords: innovation studies; science policy; challenges; achievements; dark innovation Acknowledgements A preliminary version of this paper was presented at the Lundvall symposium held at Aalborg University in February 2012. A short version (based on 15 challenges rather than 20) is being published, along with other contributions to that event, in a book on The Future of Innovation Studies (Fagerberg et al., 2013).