With rapid increase in computing power, recent petascale direct numerical simulations (DNS) have been performed of canonical turbulent configurations to glean physical insight into ‘turbulence-chemistry’ interactions in combustion and to provide validation data for the development of coarse-grained engineering models. The role of DNS is illustrated through two examples where turbulence is affected by combustion. In the first example, DNS of turbulent hydrogen/air premixed flames interacting with intense shear driven turbulence in a planar jet is used to study inter-scale energy transfer through one-dimensional auto- and cross-correlation functions and corresponding spectra of reactive scalars from the turbulent premixed flames. Balance equations for the density weighted turbulent kinetic energy and scalar fluctuation spectra for reacting flows are derived and used to understand the physical processes unique to reacting flows.  In the second example, DNS focused on the characterization of flashback for premixed, preheated hydrogen-air flames in turbulent boundary layers show that one of the principal assumptions behind the widely-used flashback model of Lewis and Von Elbe is flawed.  In this model the effect of the premixed flame on the approaching flow is negligible, while the DNS and also recent experiments reveal the presence of flow reversals, induced by the combustion in the viscous layer located immediately upstream of flame surface regions that are convex towards the reactants.  This finding suggests a radically different picture about the mechanism of boundary layer flashback and a need for a near-wall flame propagation model that correctly accounts for the combustion effect on the oncoming turbulence. Finally, the challenges and prospects for DNS of turbulent combustion at the exascale will be discussed in the context of co-design of numerical algorithms, the software stack, and computer architectures.