Data is increasingly organised as networks. Visualisation is a key way to understand networks. We plan to develop a new paradigm for this task. Using modern generic constrained optimisation techniques we will produce layouts for small graphs whose quality is similar to that produced by hand, something that is not possible with current approaches. We will then use these algorithms to visualise large graphs. Instead of simply trying to visualise every node and link in the graph we will develop techniques to extract useful subsets or abstractions that are as small possible, yet sufficient to answer targeted queries. Our techniques for producing small high-quality diagrams will then be applicable to presenting these focused visualisations.