The complex, dynamic shock-detonation structure formed by the glancing interaction of a primary detonation with a secondary explosive is studied by using time-dependent two-dimensional simulations and related experiments. The materials considered in the simulations are stoichiometric and lean mixtures of hydrogen and oxygen diluted with argon. Related experiments have used undiluted hydrogen and oxygen as well as other gases. For the conditions simulated: (a) the primary mixture is stoichiometric and the secondary inert; (b) both the primary and secondary mixtures are the same and stoichiometric; (c) the primary mixture is lean and the secondary is stoichiometric; and (d) the primary mixture is stoichiometric and the secondary is lean. In addition, for cases (b) and (d), comparisons are made between simulations in which the primary mixture is overdriven and when it is a Chapman-Jouguet detonation. For the overdriven stoichiometric primary detonation interacting with the lean mixture, a complex detonation structure forms and quickly asymptotes to the detonation velocity of the primary mixture. For this same case, but when the primary detonation is initially at Chapman-Jouguet velocity, the detonation appears to die but then reignites due to a series of shock reflections and then propagates as a complex structure. The lowest velocity of the complex structure is always greater than the Chapman-Jouguet velocity of the lean mixture and it increases in time, appearing to approach the Chapman-Jouguet velocity of the stoichiometric mixture. The dynamics of this decay and reignition process are described and discussed in detail.