When the detonation reaction-zone length, {eta}{sub r}, is short in comparison to the dimensions of the explosive piece being burnt, the detonation can be viewed as a propagating surface (or front) separating burnt from unburnt material. If the product of the shock curvature, {kappa} and {eta}{sub r} is small (i.e., the scaled shock curvature satisfies the {vert_bar}{kappa}{eta}{sub r}{vert_bar} {much_lt} 1), then to leading order the speed of this surface, D{sub n}({kappa}) is a function only of {kappa}. It is in this limit that the original version of the asymptotic detonation front theory, called detonation shock dynamics (DSD), derives the propagation law, D{sub n}({kappa}). In this lecture, the authors compare D{sub n}({kappa})-theory with the results obtained with high-resolution direct numerical simulations (DNS), and then use the DNS results to guide the development of extended asymptotic front theories with enhanced predictive capabilities
