In cold dark matter cosmological models , structures form and grow by merging of smaller units. Numerical simulations have shown that such merging is incomplete; the inner cores of halos survive and orbit as “subhalos” within their hosts . Here we report a simulation that resolves such substructure even in the very inner regions of the Galactic halo. We find hundreds of very concentrated dark matter clumps surviving near the solar circle, as well as numerous cold streams. The simulation reveals the fractal nature of dark matter clustering: Isolated halos and subhalos contain the same relative amount of substructure and both have cuspy inner density profiles. The inner mass and phase-space densities of subhalos match those of recently discovered faint, dark matter-dominated dwarf satellite galaxies, and the overall amount of substructure can explain the anomalous flux ratios seen in strong gravitational lenses . Subhalos boost gamma-ray production from dark matter annihilation, by factors of 4-15, relative to smooth galactic models. Local cosmic ray production is also enhanced, typically by a factor 1.4, but by more than a factor of ten in one percent of locations lying sufficiently close to a large subhalo. These estimates assume that gravitational effects of baryons on dark matter substructure are small.