The consequences of nuclear black holes for the structure and dynamics of stellar spheroids are reviewed. Slow growth of a black hole in a pre-existing core produces a power-law cusp, p~ r−y, with y~ 2, similar to the steep cusps seen in faint elliptical galaxies. The weaker cusps in bright ellipticals, y<~1, may result from ejection of stars by a coalescing black-hole binary; there is marginal kinematical evidence for such a process having occurred in M87. Stellar orbits in a triaxial nucleus are mostly regular at radii where the gravitational force is dominated by the black hole, r<~rg; however the orbital shapes are not conducive to reinforcing the triaxial figure, hence nuclei are likely to be approximately axisymmetric. In triaxial potentials, a “zone of chaos” extends from a few times rg out to a radius where the enclosed stellar mass is ~102 times the mass of the black hole; in this chaotic zone, no regular, box-like orbits exist. At larger radii, the phase space in triaxial potentials is complex, consisting of stochastic orbits as well as regular orbits associated with stable resonances. Figure rotation tends to increase the degree of stochasticity. Both test-particle integrations and N-body simulations suggest that a triaxial galaxy responds globally to the presence of a central mass concentration by evolving toward more axisymmetric shapes; the evolution occurs rapidly when the mass of the central object exceeds ~2% of the mass in stars. The lack of significant triaxiality in most early-type galaxies may be a consequence of orbital evolution induced by nuclear black holes [for exact p, r and y forms and other formulas see attached document].