  We review some recent work in fast, efficient and accurate methods to compute
viscosity solutions and non-viscosity solutions to static Hamilton-Jacobi
equations which arise in optimal control, anisotropic front propagation, and
multiple arrivals in wave propagation. For viscosity solutions, the class of
algorithms are known as ``Ordered Upwind Methods'', and rely on a systematic
ordering inherent in the characteristic flow of information. For non-viscosity
multiple arrivals, the techniques hinge on a static boundary value phase-space
formulation which again can be solved through a systematic ordering.
