This paper overviews the approach of the Elastic Networks research network to address the challenges posed by the convergence of networking and computing in the edge for a number of scenarios. Each section of the paper covers one topic addressed by the network. Firstly, we address reliability in Fog-to-Cloud computing (F2C). Then, an architecture for a residential SDN gateway featuring NFV is presented. In addition, switching based on SDN for data centres is studied for which a high-speed flexible packet matching in hardware is proposed. Resiliency in SDN controller location is also addressed. Finally, a technique for delay analysis in a single node C-RAN scenario is described.