In this chapter we will argue that studying such multi-scale multi-science systems gives rise to inherently hybrid models containing many different algorithms best serviced by different types of computing environments (ranging from massively parallel computers, via large-scale special purpose machines to clusters of PC's) whose total integrated computing capacity can easily reach the PFlop/s scale. Such hybrid models, in combination with the by now inherently distributed nature of the data on which the models `feed' suggest a distributed computing model, where parts of the multi-scale multi-science model are executed on the most suitable computing environment, and/or where the computations are carried out close to the required data (i.e. bring the computations to the data instead of the other way around). We presents an estimate for the compute requirements to simulate the Galaxy as a typical example of a multi-scale multi-physics application, requiring distributed Petaflop/s computational power.