Turbulent combustion represents an enormous computational challenge because of the multiple scales involved: from the large scales of interest of engineers down to the smallest scales related to turbulence fluctuations, and the even smaller ones associated with the flame thickness. I will introduce some key ideas on how to tackle this challenge for an idealized test-case of a multiple-scale advection- reaction-diffusion equation. The first testproblem will be linked to premixed flames, where the challenge is to predict the speed of propagation and the shape of a very thin, very distorted flame front. Those overall features of the flame dynamics depend very much on resolving the detailed behavior down to the smallest scales. In a traditional adaptive mesh strategy, the pde would be discretized in a nested set of grids of increasing resolution, with the solution on the different meshes tightly coupled. An asymptotic study however reveals that tight coupling is not required: I will describe a loosely-coupled grids strategy designed to exploit the asymptotic results for greater efficiency. The second test-problem will be linked to nonpremixed flames. As in the first example, a practical strategy to deal with the computational challenge is to decouple to some extent the computation at large and small scales - this leads to the socalled steady laminar flamelet model. As indicated by the name, one major assumption is that the smallest scales behave as if the problem was steady. A test- case is set-up to validate this type of strategy in a case with extreme unsteady, intermittent behavior that reflects more realistic turbulent conditions. The validation requires a very accurate time-integrator. I will describe a very convenient approach to design a high order time integrator for advection-reaction- diffusion equation. It is a multi-implicit, split, scheme where high order is achieved via spectral deferred correction. It is built upon simple backward Euler schemes and very easy to implement; it also leads very naturally to timestep adaptation.