Accurate diagnosis of disease is of fundamental importance in clinical practice and medical research. Before a medical diagnostic test is routinely used in practice, its ability to distinguish between diseased and nondiseased states must be rigorously assessed. The receiver operating characteristic (ROC) curve is the most popular used tool for evaluating the diagnostic accuracy of continuous-outcome tests. It has been acknowledged that several factors (e.g., subject-specific characteristics such as age and/or gender) can affect the test outcomes and accuracy beyond disease status. Recently, the covariate-adjusted ROC curve has been proposed and successfully applied as a global summary measure of diagnostic accuracy that takes covariate information into account. The aim of this paper is three-fold. First, we motivate the importance of including covariate-information, whenever available, in ROC analysis and, in particular, how the covariate-adjusted ROC curve is an important tool in this context. Second, we review and provide insight on the existing approaches for estimating the covariate-adjusted ROC curve. Third, we develop a highly flexible Bayesian method, based on the combination of a Dirichlet process mixture of additive normal models and the Bayesian bootstrap, for conducting inference about the covariate-adjusted ROC curve. A simulation study is conducted to assess the performance of the different methods and it also demonstrates the ability of our proposed Bayesian model to successfully recover the true covariate-adjusted ROC curve and to produce valid inferences in a variety of complex scenarios. The methods are applied to an endocrine study where the goal is to assess the accuracy of the body mass index, adjusted for age and gender, for detecting clusters of cardiovascular disease risk factors.