  In this paper I will outline some of the aspects and problems of modern
celestial mechanics and stellar dynamics, in the context of the quickly growing
computing facilities. I will point the attention on the great advantages in
using, for astrophysical simulations, the modern, fast and cheap Graphic
Processing Units (GPUs) acting as true supercomputers. Finally, I present and
discuss some characteristics and performances of a new double-parallel code
exploiting the joint power of multicore CPUs and GPUs.
