The structure of premixed turbulent flames is a problem of fundamental interest in combustion theory. Possible flame geometries have been imagined and diagrams indicating the corresponding regimes of combustion have been constructed on the basis of essentially intuitive and dimensional considerations. A new approach to this problem is described in the present paper. An extended definition of flamelet regimes based on the existence of a continuous active (not quenched) flame front separating fresh gases and burnt products is first introduced. Direct numerical simulations of flame/vortex interactions using the full Navier–Stokes equations and a simplified chemistry model are then performed to predict flame quenching by isolated vortices. The formulation includes non-unity Lewis number, non-constant viscosity and heat losses so that the effect of stretch, curvature, transient dynamics and viscous dissipation can be accounted for. As a result, flame quenching by vortices (which is one of the key processes in premixed turbulent combustion) may be computed accurately. The effects of curvature and viscous dissipation on flame/vortex interactions may also be characterized by the same simulations. The influence of non-unity Lewis number and of thermo-diffusive processes in turbulent premixed combustion is discussed by comparing flame responses for two values of the Lewis number (Le = 0.8 and 1.2). An elementary (‘spectral’) diagram giving the response of one flame to a vortex pair is constructed. This spectral diagram is then used, along with certain assumptions, to establish a turbulent combustion diagram similar to those proposed by Borghi (1985) or Williams (1985). Results show that flame fronts are much more resistant to quenching by vortices than expected from the classical theories. A cut-off scale and a quenching scale are also obtained and compared with the characteristic scales proposed by Peters (1986). Results show that strain is not the only important parameters determining flame/vortex interaction. Heat losses, curvature, viscous dissipation and transient dynamics have significant effects, especially for small scales and they strongly influence the boundaries of the combustion regimes. It is found, for example, that the Klimov–Williams criterion which is generally advocated to limit the flamelet region, underestimates the size of this region by more than an order of magnitude.