For the past thirty years, the need for ever greater supercomputer performance has driven the development of many computing technologies which have subsequently been exploited in the mass market. Delivering an exaflop (or 10^18 calculations per second) by the end of this decade is the challenge that the supercomputing community worldwide has set itself. The Collaborative Research into Exascale Systemware, Tools and Applications project (CRESTA) brings together four of Europe's leading supercomputing centres, with one of the world's major equipment vendors, two of Europe's leading programming tools providers and six application and problem owners to explore how the exaflop challenge can be met. CRESTA focuses on the use of six applications with exascale potential and uses them as co-design vehicles to develop: the development environment, algorithms and libraries, user tools, and the underpinning and cross-cutting technologies required to support the execution of applications at the exascale. The applications represented in CRESTA have been chosen as a representative sample from across the supercomputing domain including: biomolecular systems, fusion energy, the virtual physiological human, numerical weather prediction and engineering.No one organisation, be they a hardware or software vendor or service provider can deliver the necessary range of technological innovations required to enable computing at the exascale. This is recognised through the on-going work of the International Exascale Software Project and, in Europe, the European Exascale Software Initiative. CRESTA will actively engage with European and International collaborative activities to ensure that Europe plays its full role worldwide. Over its 39 month duration the project will deliver key, exploitable technologies that will allow the co-design applications to successfully execute on multi-petaflop systems in preparation for the first exascale systems towards the end of this decade.