A science-based understanding of combustion facilitates the design of more efficient engines with more carefully controlled emissions. A fully predictive, first principles computational model of an internal combustion engine can now be imagined, although many challenges remain before such a model exists. Several new and ongoing multi-institutional programs designed to address these challenges are underway, coordinating scientists from different fields and levels of this multi-scale problem. One motivation for this session is to bring together world leaders from some of these programs, with an emphasis on discussing predicting the complex chemistry of combustion. Although the governing reaction of combustion is simple (fuel + oxygen → water + carbon dioxide + energy), combustion in fact involves thousands of intermediate chemical species. A fully predictive combustion model requires the enumeration of the important reactions from among the many thousands of possible ones, as well as the ability to predict from first principles the rates and products of these reactions. In this symposium, we address the following questions: How accurate are first principles chemical kinetics calculations for processes relevant to the combustion of real fuels, and how accurate do they need to be for useful and predictive modeling? What new strategies are needed to go forward? How can we identify where to best focus future computational efforts? How close are we to fully predictive models of combustion chemistry?