This paper describes recent progress in the field of Direct Numerical Simulations (DNS) for premixed turbulent combustion. A classification of Computational Fluid Dynamics techniques used in reacting flows is first proposed. Numerical methods and problems specific to DNS of combustion like grid resolution or boundary conditions treatment are discussed. The presentation of DNS results is done in the framework of flamelet modeling. The domain of validity of the flamelet assumptions is studied with simulations of flame vortex interactions. The local structure of flamelets in premixed turbulent combustion is investigated using two and three-dimensional DNS with simple chemistry models. Effects of complex chemistry are considered through recent two-dimensional DNS performed with realistic chemical schemes. Flame surface densities, flame strain and curvature statistics obtained from various three dimensional simulations are given and implications for modeling are presented. DNS is also exploited to deal with some specific problems like turbulent flame ignition or flame-wall interactions. This review is concluded with a discussion of current limitations and a list of future challenges.