|Abstract:|| In the context of Large Eddy Simulation (LES) of turbulent flows, only the more energetic scales of motions are represented while the effect of the smaller ones is modelled. For complex and unsteady flows, it is difficult to set a priori the numerical resolution corresponding to the scales that must be directly simulated. Adaptive (in the polynomial or grid sense) LES should overcome this problem allowing to locally adapt the discretization resolution to simulate a necessary amount of the turbulent scales. The present talk is focused on the polynomial degree adaptation in a discontinuous Galerkin method. The polynomial adaptivity procedure is quite established for non turbulent phenomena, and usually relies on a suitable local error estimation. In a turbulent flows this approach should lead to a convergence towards the direct numerical simulation (DNS), in contrast with the aim of a LES. In the present talk different approaches will be presented and discussed.