Combustion currently provides 85% of our nation’s energy needs. Furthermore, because of the large infrastructure costs combustion will continue to be the predominant source of energy for the near and middle term. Concerns over U.S. dependence on imported oil coupled with pollution and greenhouse gas emission issues require that we develop a new generation of combustion systems that provide both high efficiency and low emissions. As design requirements become more stringent there is a need for improved models that provide high-fidelity predictive capability for engineering studies. Terascale and petascale high-fidelity simulations of turbulent combustion flows are poised to address complex multi-physics, multi-scale interactions, such as the so-called “turbulence-chemistry” interactions in combustion flows. Using an approach known as direct numerical simulation, where all relevant fluids and chemical scales are numerically resolved, underlying phenomena in devices can be uniquely understood and modelled, e.g. autoignition of thermally stratified lean mixtures in a homogeneous charge compression ignition engine environment, extinction and reignition in turbulent jet flames, and lean premixed flame structure in turbulent Bunsen flames. Results from recent terascale DNS simulations of turbulent combustion will be presented to illustrate cyberinfrastructure requirements for combustion science. Significant challenges remain to extract salient information from terascale combustion data sets, and to manage data movement, storage, workflow and data sharing over the wide-area-network.