Abstract: Galaxies are embedded in diffuse halos of dark matter that must consist of particles or objects whose non-gravitational interactions are constrained to be extremely weak. The dynamics of dark-matter halos have traditionally been studied with N-body simulations that evolve the 6-dimensional (three spatial dimensions plus 3 velocity dimensions) phase-space distribution. However, if the halo can be approximated as spherically symmetric, then there is a far more computationally efficient approach. I will discuss the dark-matter problem, the gravitational dynamics of dark-matter halos, and this new approach. I will illustrate its utility by showing results for models in which dark matter decays or has self-interactions, where the gravitational constant evolves, or the halo is tidally stripped.