Despite decades of research, brain tumours remain among the deadliest of all forms of cancer. The ability of these tumours to resist almost all conventional and novel treatments relates, in part, to the unique cell-intrinsic and microenvironmental properties of neural tissues. In an attempt to encourage progress in our understanding and ability to successfully treat patients with brain tumours, Cancer Research UK convened an international panel of clinicians and laboratory-based scientists to identify challenges that must be overcome if we are to cure all patients with a brain tumour. The seven key challenges summarized in this Position Paper are intended to serve as foci for future research and investment. © 2019, Springer Nature Limited.