A reaction is called "explosive" when the amount of a reactant becomes infinite in a finite time. When the intrinsic stochastic character of the reaction is taken into account, the explosion time is a random quantity. We compute its probability distribution, or at least its average and variance, for various kinds of reactions. If a reaction is unstable, so that a reactant can either explode or disappear, one first has to compute the probability for an explosion to occur at all, and then the average explosion time. Finally, the same ideas are applied to more general Markov processes.