This paper presents numerical simulations of dark matter substructure within galactic and cluster halos in a hierarchical universe. The simulations show that clusters can be well-reproduced with a steep mass spectrum of thousands of substructure clumps, matching observations. However, dark matter substructure also survives on galactic scales, leading to the remarkable result that galaxy halos appear as scaled versions of galaxy clusters. The model predicts that the Milky Way's halo should contain about 500 satellites with circular velocities larger than Draco and Ursa Minor, i.e., bound masses greater than 10^8 solar masses and tidal sizes greater than kiloparsecs. These substructure clumps orbit through the stellar disk, causing significant resonant and impulsive heating. Their abundance and density profiles have important implications for the existence of old thin disks, cold stellar streams, gravitational lensing, and dark matter detection experiments. The paper discusses the formation of dark matter halos in a hierarchical universe, where galaxies form by a similar merging and accretion process as clusters. Over-merging on galactic scales is a necessary requirement, otherwise previous generations of the hierarchy would preclude the formation of disks. Observations suggest that over-merging has been nearly complete on galactic scales. The Milky Way contains just 11 satellites within its virial radius with a velocity dispersion ratio of 0.07, equivalent to a velocity dispersion of 10 km/s. In a rich cluster, there are 500-1000 such systems. The same discrepancy exists at higher masses. The Coma cluster contains more than 30 galaxies brighter than the characteristic break in the luminosity function, L* ≡ σ > 200 km/s. Scaling this limit to a galaxy halo, we find just 2 satellites in the Milky Way or 3 near Andromeda. The paper also discusses the implications of dark matter substructure for the formation of galaxies and the observed properties of galaxy halos. It shows that the distribution of circular velocities for the model galaxy and cluster can be fitted with a power law, similar to that found for satellites in galactic halos. The mass function within these systems can be approximated by a power law. The tidally limited substructure halos have profiles close to isothermal spheres with core radii equal to our resolution length. Increasing the resolution only makes the halos denser and more robust to disruption. The paper concludes that either the hierarchical model is fundamentally wrong, or the substructure lumps are present in the galactic halo and contain too few baryons to be observed. The deficiency of satellites in galactic halos is similar to a deficiency of dwarf galaxies in the field. One possibility is that some of the missing satellites may be linked to the high velocity clouds. Numerous studies have invoked feedback from star formation or an ionizing background to darken dwarfs by expelling gas and inhibiting starThis paper presents numerical simulations of dark matter substructure within galactic and cluster halos in a hierarchical universe. The simulations show that clusters can be well-reproduced with a steep mass spectrum of thousands of substructure clumps, matching observations. However, dark matter substructure also survives on galactic scales, leading to the remarkable result that galaxy halos appear as scaled versions of galaxy clusters. The model predicts that the Milky Way's halo should contain about 500 satellites with circular velocities larger than Draco and Ursa Minor, i.e., bound masses greater than 10^8 solar masses and tidal sizes greater than kiloparsecs. These substructure clumps orbit through the stellar disk, causing significant resonant and impulsive heating. Their abundance and density profiles have important implications for the existence of old thin disks, cold stellar streams, gravitational lensing, and dark matter detection experiments. The paper discusses the formation of dark matter halos in a hierarchical universe, where galaxies form by a similar merging and accretion process as clusters. Over-merging on galactic scales is a necessary requirement, otherwise previous generations of the hierarchy would preclude the formation of disks. Observations suggest that over-merging has been nearly complete on galactic scales. The Milky Way contains just 11 satellites within its virial radius with a velocity dispersion ratio of 0.07, equivalent to a velocity dispersion of 10 km/s. In a rich cluster, there are 500-1000 such systems. The same discrepancy exists at higher masses. The Coma cluster contains more than 30 galaxies brighter than the characteristic break in the luminosity function, L* ≡ σ > 200 km/s. Scaling this limit to a galaxy halo, we find just 2 satellites in the Milky Way or 3 near Andromeda. The paper also discusses the implications of dark matter substructure for the formation of galaxies and the observed properties of galaxy halos. It shows that the distribution of circular velocities for the model galaxy and cluster can be fitted with a power law, similar to that found for satellites in galactic halos. The mass function within these systems can be approximated by a power law. The tidally limited substructure halos have profiles close to isothermal spheres with core radii equal to our resolution length. Increasing the resolution only makes the halos denser and more robust to disruption. The paper concludes that either the hierarchical model is fundamentally wrong, or the substructure lumps are present in the galactic halo and contain too few baryons to be observed. The deficiency of satellites in galactic halos is similar to a deficiency of dwarf galaxies in the field. One possibility is that some of the missing satellites may be linked to the high velocity clouds. Numerous studies have invoked feedback from star formation or an ionizing background to darken dwarfs by expelling gas and inhibiting star