Network slicing has emerged as a major new networking paradigm for meeting the diverse requirements of various vertical businesses in virtualised and softwarised 5G networks. SliceNet is a project of the EU 5G Infrastructure Public Private Partnership (5G PPP) and focuses on network slicing as a cornerstone technology in 5G networks, and addresses the associated challenges in managing, controlling and orchestrating the new services for users especially vertical sectors, thereby maximising the potential of 5G infrastructures and their services by leveraging advanced software networking and cognitive network management. This paper presents the vision of the SliceNet project, highlighting the gaps in existing work and challenges, the proposed overall architecture, proposed technical approaches, and use cases.