Systems biology is based on computational modelling and simulation of large networks of interacting components. Models may be intended to capture processes, mechanisms, components and interactions at different levels of fidelity. Input data are often large and geographically disperse, and may require the computation to be moved to the data, not vice versa. In addition, complex system-level problems require collaboration across institutions and disciplines. Grid computing can offer robust, scaleable solutions for distributed data, compute and expertise. We illustrate some of the range of computational and data requirements in systems biology with three case studies: one requiring large computation but small data (orthologue mapping in comparative genomics), a second involving complex terabyte data (the Visible Cell project) and a third that is both computationally and data-intensive (simulations at multiple temporal and spatial scales). Authentication, authorisation and audit systems are currently not well scalable and may present bottlenecks for distributed collaboration particularly where outcomes may be commercialised. Challenges remain in providing lightweight standards to facilitate the penetration of robust, scalable grid-type computing into diverse user communities to meet the evolving demands of systems biology.