This review paper addresses the following question: what is the structure of flamelets within premixed turbulent combustion and how does this structure affect the turbulent burning velocity? We also ask: how accurately can new models predict the flamelet structure as well as the values of turbulent burning velocity? Flamelet structure is defined to include the following quantities: reaction layer surface area per unit volume (Sigma), the brush thickness (delta(T)) and the stretch factor (I-0). One equation that is commonly used to relate these flamelet structure parameters to the burning velocity S-T is
ST/SL0 = I-0 (-infinity)integral(infinity) Sigma d eta = I-0 Sigma(max)delta(T.)
Recent results obtained using laser imaging methods and direct numerical simulation (DNS) are reviewed in order to demonstrate the relationships between S-T, Sigma, I-0 and delta(T). eta is the direction normal to the brush. Measurements of Sigma show that the wrinkling process is not local but has a "memory" of wrinkling that occurs elsewhere. The stretch factor I-0 depends on differential diffusion (Markstein number) even at large turbulence intensities. Thus the concepts associated with the theory of flame stretch have been found to be valid even for highly turbulent flames. Thin flamelets exist for nearly all cases for which images of the reaction zone have been obtained. Evidence of "non-flamelet" behavior is sparse. DNS now can successfully predict realistic values of turbulent burning velocity for laboratory-scale Reynolds numbers and for the realistic geometries of Bunsen and V-flames using complex chemistry and no empirical constants. Large eddy simulations (LES) also have predicted reasonable values Of ST, but some empirical constants are required. A number of current research issues are discussed.