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In this review, we present an overview of the main aspects related to the statistical evaluation of medical tests for diagnosis and prognosis. Measures of diagnostic performance for binary tests, such as sensitivity, specificity, and predictive values, are introduced, and extensions to the case of continuous-outcome tests are detailed. Special focus is placed on the receiver operating characteristic (ROC) curve and its estimation, with the topic of covariate adjustment receiving a great deal of attention. The extension to the case of time-dependent ROC curves for evaluating prognostic accuracy is also touched upon. We apply several of the approaches described to a dataset derived from a study aimed to evaluate the ability of HOMA-IR (homeostasis model assessment of insulin resistance) levels to identify individuals at high cardio-metabolic risk and how such discriminatory ability might be influenced by age and gender. We also outline software available for the implementation of the methods.