Recent theoretical results on the dynamics of gaseous detonations are presented. An asymptotic analysis is performed, retaining the physical mechanisms controlling the modifications to the inner structure of the detonation. As a result, the system of hyperbolic equations for the compressible fluid mechanics coupled with a detailed chemical kinetics of heat release is reduced to a single integral equation for the propagation velocity of the combustion wave versus time. Concerning the direct initiation of spherical detonations by a blast wave, curvature effects are shown to be responsible for a critical condition of initiation. Near criticality, the role of the unsteadiness of the inner structure is pointed out. The whole complexity of the critical dynamics is reproduced and explained by the integral equation. The necessary background knowledge in gaseous detonation is recalled in the two first sections of the article in order to facilitate the reading by non-specialists.