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The propagation of premixed flames in turbulent flows is a problem of wide physical and technological interest, with a significant literature on their propagation speed and front topology. While certain scalings and parametric dependencies are well understood, a variety of problems remain. One major challenge, and focus of this thesis, is to model the influence of fuel/oxidizer composition on turbulent burning rates. Classical explanations for augmentation of turbulent burning rates by turbulent velocity fluctuations rely on global arguments - i.e., the turbulent burning velocity increase is directly proportional to the increase in flame surface area and mean local burning rate along the flame. However, the development of such global approaches is complicated by the abundance of phenomena influencing the propagation of turbulent premixed flames. Emphasizing key governing processes and cutting-off interesting but marginal phenomena appears to be necessary to make further progress in understanding the subject. An alternative approach to understand turbulent augmentation of burning rates is based upon so-called "leading points", which are intrinsically local properties of the turbulent flame. Leading points concepts suggest that the key physical mechanism controlling turbulent burning velocities of premixed flames is the velocity of the points on the flame that propagate farthest out into the reactants. It is postulated that modifications in the overall turbulent combustion speed depend solely on modifications of the burning rate at the leading points since an increase (decrease) in the average propagation speed of these points causes more (less) flame area to be produced behind them. In this framework, modeling of turbulent burning rates can be thought as consisting of two sub-problems: the modeling of (1) burning rates at the leading points and of (2) the dynamics/statistics of the leading points in the turbulent flame. The main objective of this thesis is to critically address both aspects, providing validation and development of the physical description put forward by leading point concepts. To address the first sub-problem, a comparison between numerical simulations of one-dimensional laminar flames in different geometrical configurations and statistics from a database of direct numerical simulations (DNS) is detailed. In this thesis, it is shown that the leading portions of the turbulent flame front display a structure that on average can be reproduced reasonably well by results obtained from model geometries with the same curvature. However, the comparison between model laminar flame computations and highly curved flamelets is complicated by the presence of negative (i.e., compressive) strain rates, due to gas expansion. For the highest turbulent intensity investigated, local consumption speeds, curvatures, strain rates and flame thicknesses approach the maximum values obtained by the laminar model geometries, while other cases display substantially lower values. To address the second sub-problem, the dynamics of flame propagation in simplified flow geometries is studied theoretically. Utilizing results for Hamilton-Jacobi equations from the Aubry-Mather theory, it is shown how the overall flame front progation under certain conditions is controlled only by discrete points on the flame. Based on these results, definitions of leading points are proposed and their dynamics is studied. These results validate some basic ideas from leading points arguments, but also modify them appreciably. For the simple case of a front propagating in a one-dimensional shear flow, these results clearly show that the front displacement speed is controlled by velocity field characteristics at discrete points on the flame only when the amplitude of the shear flow is sufficiently large and does not vary too rapidly in time. However, these points do not generally lie on the farthest forward point of the front. On the contrary, for sufficiently weak or unsteady flow perturbations, the front displacement speed is not controlled by discrete points, but rather by the entire spatial distribution of the velocity field. For these conditions, the leading points do not have any dynamical significance in controlling the front displacement speed. Finally, these results clearly show that the effects of flame curvature sensitivity in modifying the front displacement speed can be successfully interpreted in term of leading point concepts.