Named Entity Recognition systems achieve remarkable performance on domains such as English news. It is natural to ask: What are these models actually learning to achieve this? Are they merely memorizing the names themselves? Or are they capable of interpreting the text and inferring the correct entity type from the linguistic context? We examine these questions by contrasting the performance of several variants of LSTM-CRF architectures for named entity recognition, with some provided only representations of the context as features. We also perform similar experiments for BERT. We find that context representations do contribute to system performance, but that the main factor driving high performance is learning the name tokens themselves. We enlist human annotators to evaluate the feasibility of inferring entity types from the context alone and find that, while people are not able to infer the entity type either for the majority of the errors made by the context-only system, there is some room for improvement. A system should be able to recognize any name in a predictive context correctly and our experiments indicate that current systems may be further improved by such capability.