The current interest in the combustion chemistry of hydrocarbon fuels, including the various alcohol and biodiesel compounds, motivates this review of the methods and application of kinetic uncertainty quantification (UQ). Our intent is to provide a self-contained review about the mathematical principles and methods of uncertainty quantification and their application in highly complex, multi-parameter combustion chemistry problems. We begin by outlining the reasons why the kinetic uncertainty must be considered and treated as a part of the combustion chemistry development in order to make progress. This is followed by a brief discussion about the sources and classification of kinetic uncertainties and the meanings and definitions of model verification and validation. We discuss the histories of UQ studies with an emphasis on how the combustion community has a long tradition of UQ consideration through standard sensitivity analysis. Such efforts have motivated the advancements of UQ methods specifically tailored to combustion chemistry. They also led to the recent growing interests in applying UQ methods as a part of our recommended long-term solution to the chemical kinetic problem of combustion. We then review and classify the various UQ methods and illustrate their applications for problems involving forward uncertainty quantification and propagation, and as an inverse problem leading to model uncertainty constraining. For the inverse problem, the focus of discussion is in the use of methods originating from Bayes' Theorem. We show that, for combustion chemistry problems, while UQ alone cannot produce precise, individual rate parameters, it can be instrumental in measuring the progress of our understanding of combustion chemistry and in utilizing fundamental combustion property data beyond a simple "agree-disagree" statement. When treated as a Bayesian inference problem, UQ also aids the development of predictive kinetic models in two ways: the use of fundamental combustion property data, global or local, to provide a better constrained kinetic model, and along with forward kinetic uncertainty propagation, to yield estimates for the confidence of a model to make predictions outside of the thermodynamic regimes where the model has been tested. We provide several examples to illustrate the utility of the UQ methods discussed and to demonstrate that, in the field of combustion chemistry, further progress will be better achieved through a combination of fundamental studies of reaction rates through well-defined and designed experiments and ab initio theoretical calculations, and of analyses of global experimental measurements. These studies together must be supplemented by UQ analyses, in such a way that a measurable progress can be made over time. (C) 2014 Elsevier Ltd. All rights reserved.