  Spin-density-functional theory (SDFT) is the most widely implemented and
applied formulation of density-functional theory. However, it is still finding
novel applications, and occasionally encounters unexpected problems. In this
paper we first briefly describe a few of the latter, related to issues such as
nonuniqueness, noncollinearity, and currents. In the main part we then turn to
an example of the former, namely SDFT for the Heisenberg model. It is shown
that time-honored concepts of Coulomb DFT, such as the local-density
approximation, can be applied to this (and other) model Hamiltonians, too, once
the concept of 'density' has been suitably reinterpreted. Local-density-type
approximations for the inhomogeneous Heisenberg model are constructed.
Numerical applications to finite-size and impurity systems demonstrate that DFT
is a computationally efficient and reasonably accurate alternative to
conventional methods of statistical mechanics for the Heisenberg model.
