Radiologists and other qualified physicians need to examine and interpret large numbers of medical images daily. Systems that would help them spot and report abnormalities in medical images could speed up diagnostic workflows. Systems that would help exploit past diagnoses made by highly skilled physicians could also benefit their more junior colleagues. A task that systems can perform towards this end is medical image classification, which assigns medical concepts to images. This task, called Concept Detection, was part of the ImageCLEF 2019 competition. We describe the methods we implemented and submitted to the Concept Detection 2019 task, where we achieved the best performance with a deep learning method we call ConceptCXN. We also show that retrieval-based methods can perform very well in this task, when combined with deep learning image encoders. Finally, we report additional post-competition experiments we performed to shed more light on the performance of our best systems. Our systems can be installed through PyPi as part of the BioCaption package.