Artificial intelligence (AI)-based methods are showing promise in multiple medical-imaging applications. Thus, there is substantial interest in clinical translation of these methods, requiring in turn, that they be evaluated rigorously. In this paper, our goal is to lay out a framework for objective task-based evaluation of AI methods. We will also provide a list of tools available in the literature to conduct this evaluation. Further, we outline the important role of physicians in conducting these evaluation studies. The examples in this paper will be proposed in the context of PET with a focus on neural-network-based methods. However, the framework is also applicable to evaluate other medical-imaging modalities and other types of AI methods.