One of the more mature instances of a serviceoriented architecture is the model known as Grid Computing. Computational Grids and Data Grids are becoming commonplace in certain sectors, yet the style of security they implement is suitable only for a fairly small subset of possible user communities. Using some case studies and experience, we describe the existing Grid security models, explain why they represent shortcomings for some applications, and describe some emerging architectures, Trusted Computing and virtualisation, which help address the problems.