Applied mathematics sits at the convergence of collaborative modelling and data research. Its role is fundamental to how we understand our world and develop new technologies. Many applied mathematicians see new challenges as an opportunity to expand their mathematical horizon, and in our rapidly changing society, such new challenges abound. ‘Where are we going? Networks and the brain’ considers recent developments in applied mathematics such as network theory, used in modelling the internet and for studying epidemiology, and its use in studying the brain, an organ of extreme complexity. Applied mathematics is being used to create a mathematical theory of the brain, which is crucial for understanding of a host of neurological conditions.