It is increasingly evident that a sustainable use of the sea and of technologies and services that support this sustainability are fundamental for the impact they have also on the sustainability of the mainland. The Blue Growth, a knowledge driven exploitation of the marine resources, is a target that EU and many other countries have set to improve the societal wellbeing. In particular the Mediterranean has still unexploited potentials to provide very specific ecosystem services and new technologies in order to contribute to economic growth. To this aim, the European Commission funded the Bluemed project (2016-2020), which involves nine different European countries (Croatia, Cyprus, France, Greece, Italy, Malta, Portugal, Slovenia, Spain) and their relevant stakeholders in the definition of shared strategies at national and international level; the Italian National Research Council (CNR) coordinates Bluemed. Given this framework, the present paper, starts from the main outcomes of Bluemed on research and innovation in the Mediterranean, through a detailed analysis of the most relevant activities and thematic objectives for some of the main marine and maritime socio-economic drivers (transport, tourism, energy have been chosen). Then, on that basis and with the support of a deep literature overview, it tries to understand the present status of some relevant sectors for their potential impact on technology and innovation on this maritime area, highlighting the main obstacles to the fulfilment of the planned priorities and proposing possible strategies to overcome them; all this starting from an Italian perspective. The emphasis is put just on the gaps and barriers to Blue Growth, and on the ways to overcome them, to help the identification of cross-cutting high-level priorities and actions for research and innovation, to be shared at national and Mediterranean level. The main contribution of the work presented here is the recognition that concrete steps towards a "Blue" economy can be achieved only by going beyond the identification of research and innovation challenges and priorities for specific sectors, since they necessarily reflect a partial, sectorial view, and that the main effort must be directed towards an integrated view of how different activities, often conflicting, might coexists. Another finding is the planning of roadmaps to follow so that new technologies/knowledge could overcome those conflicts. As a consequence, the aim and the output of the paper is not proposing a further detailed list of Research and Innovation priorities, but is instead trying to identify how the most relevant R&I challenges for Blue Growth already available can be more efficiently pursued following the roadmaps proposed in the paper.