The modern study of the dynamics of stellar systems requires the use of high-performance computers. Indeed, an accurate modelization of the structure and evolution of self-gravitating systems like planetary systems, open clusters, globular clusters and galaxies imply the evaluation of body-body interaction over the whole size of the structure, a task that is computationally very expensive, in particular when it is performed over long intervals of time. In this report we give a concise overview of the main problems of stellar systems simulations and present some exciting results we obtained about the interaction of globular clusters with the parent galaxy.