Spin-dynamics techniques can now be used to study the deterministic time-de
pendent behavior of magnetic systems containing over 10(5) spins with quite
good accuracy. This approach will be introduced, including the theoretical
foundations of the methods of analysis. Then newly developed, improved tec
hniques based upon Suzuki-Trotter decomposition methods will be described.
The current "state-of-the-art" will be evaluated with specific examples dra
wn from data on simple magnetic models. The examination of dynamic critical
behavior will be highlighted but the extraction of information about excit
ations at low temperatures will be included.