ABSTRACT This paper describes how the framework developed for universal kriging can accommodate a general formulation of the reservoir history matching problem. We illustrate this framework with simple examples, and then show that the specification of the required covariances and correlations provides an opportunity to introduce explicitly some pertinent reservoir engineering knowledge into history matching. We then briefly consider the elicitation of this information in the form of parameter values in functional forms for covariances, and discuss how the specification of weights can influence calculations, and hence convergence to an optimal history match. We conclude with a review of some of the available diagnostics and a summary on practical applications of the framework.