The current generation of deep neural networks has achieved close-to-human results on "closed-set" image recognition; that is, the classes being evaluated overlap with the training classes. Many recent methods attempt to address the importance of the unknown, which are termed "open-set" recognition algorithms, try to reject unknown classes as well as maintain high recognition accuracy on known classes. However, it is still unclear how different general domain-trained open-set methods from ImageNet would perform on a different but more specific domain, such as the medical domain. Without principled and formal evaluations to measure the effectiveness of those general open-set methods, artificial intelligence (AI)-based medical diagnostics would experience ineffective adoption and increased risks of bad decision making. In this paper, we conduct rigorous evaluations amongst state-of-the-art open-set methods, exploring different open-set scenarios from "similar-domain" to "different-domain" scenarios and comparing them on various general and medical domain datasets.