In the field of reactive fluid dynamics, wrinkled flames are the archetype of pre-mixed flames in moderate turbulence, which can e.g. propagate in the combustion chamber of a car engine. Such kind of flames can also be seen in some factory explosions or blazes, in certain industrial burners and gas boilers, and even in the explosion of Type Ia Supernovae, the "candles of the Universe". In this context, the direct resolution of the reactive Navier-Stokes equations (i.e. including exothermic chemical kinetics processes), or DNS, requires very high spatio-temporal resolution (on Earth, these flames are very thin, of the order of a few hundred microns) as well as very sophisticated numerical methods. In addition, the accurate solution of these fronts using DNS is extremely sensitive to any perturbation, particularly of numerical origin : mesh shape, discretization and spatial integration method, temporal integration method, chemical kinetics model, etc. An alternative, simplified, asymptotic modeling for this type of phenomenon consists of establishing and numerically solving a nonlinear, non-local evolution equation for the flame front. After a brief introduction to combustion basics, difficulties, and reduced approaches, we shall present the Michelson Sivashinsky (MS) type equations (up to 3rd order). This class of equations constitute a relatively simple approach, offering the possibility of "gaining" a spatial dimension compared with the "volume" resolution of the balance equations. We shall then compare the results obtained with the simplified EEM approach, direct simulations and experiments. The presentation will conclude with a number of other possible applications, and a link with the dynamics of a random multi-scale biological network.