This paper reviews the state of the art in applying uncertainty quantification (UQ) methods to additive manufacturing (AM). Physics-based as well as data-driven models are increasingly being developed and refined in order to support process optimization and control objectives in AM, in particular to maximize the quality and minimize the variability of the AM product. However, before using these models for decision-making, a fundamental question that needs to be answered is to what degree the models can be trusted, and consider the various uncertainty sources that affect their prediction. UQ in AM is not trivial because of the complex multiphysics, multiscale phenomena in the AM process. This article reviews the literature on UQ methodologies focusing on model uncertainty, discusses the corresponding activities of calibration, verification, and validation, and examines their applications reported in the AM literature. The extension of current UQ methodologies to additive manufacturing needs to address multiphysics, multiscale interactions, increasing presence of data-driven models, high cost of manufacturing, and complexity of measurements. The activities that need to be undertaken in order to implement verification, calibration, and validation for AM are discussed. Literature on using the results of UQ activities toward AM process optimization and control (thus supporting maximization of quality and minimization of variability) is also reviewed. Future research needs both in terms of UQ and decision-making in AM are outlined.