The aim of this Report is to help policy makers working in different government levels involved in Smart Specialisation (S3) processes to understand how multilevel governance operates in their context and also how they can develop and facilitate its construction in their S3 strategies. The motivation behind this study is the belief that multilevel governance (MLG) can be improved and that S3 can be made more efficient with a win-win approach for different governments involved in the process. In order to begin this reflection, we first define the concept of multilevel governance, connect it to other relevant concepts regarding S3 and explain the place-based and experimental nature of multilevel governance, highlighting its complexity as one of its main characteristics. After describing the government levels that are actually in charge of S3 strategies under the umbrella of the European Commission, the brief focuses on its main contribution: the definition of four pillars for the construction of multilevel governance of place-based S3 strategies. We defined these pillars to help understand how multilevel governance can be built. For each of the pillars, one example linked to the Basque cases is described, together with another example from a different context, i.e. the Six City strategy in Finland, the regions of Flanders in Belgium, Extremadura in Spain, and Baden-Württemberg in Germany.