Health economic evaluation has become increasingly important in medical research and recently has been built on solid statistical and decision-theoretic foundations, particularly under the Bayesian approach. In this paper we review the basic concepts and issues associated with the statistical and decision-theoretic components of health economic evaluations. We present examples of typical models used in different contexts (depending on the availability of data). We also describe the process of uncertainty analysis, a crucial component of economic evaluations for health care interventions, aimed at assessing the impact of uncertainty in the model parameters on the final decision-making process. Finally, we discuss some of the most recent methodological developments, related with the application of advanced statistical models (e.g.~Gaussian Process regression) to facilitate the application of computationally expensive tools such as the Value of Information analysis.