  We describe recent analytical and numerical results on stability and behavior
of viscous and inviscid detonation waves obtained by dynamical systems/Evans
function techniques like those used to study shock and reaction diffusion
waves. In the first part, we give a broad description of viscous and inviscid
results for 1D perturbations; in the second, we focus on inviscid
high-frequency stability in multi-D and associated questions in turning point
theory/WKB expansion.
