. In this note we review the random projection methods, recently introduced by the authors, for numerical simulations of the hyperbolic conservation laws with stiff reaction terms: U t + F (U)x = 1 " Psi(U ): In this problem, the reaction time " is small, making the problem numerically stiff. A classic spurious numerical phenomenon -- the incorrect shock speed -- occurs when the reaction time scale is not properly resolved numerically. The random projection method, a fractional step method that solves the homogeneous convection by any shock capturing method, followed by a random projection for the reaction term, was introduced in [1] to handle this numerical difficulty. For a scalar model problem, one can prove that the random projection methods capture the correct shock speed with a first order accuracy, if a monotonicity-preserving method is used in the convection step. This method can also be extended to compute stiff detonation waves by randomizing the ignition temperature. N...