While there has been much recent work studying how linguistic information is encoded in pre-trained sentence representations, comparatively little is understood about how these models change when adapted to solve downstream tasks. Using a suite of analysis techniques (probing classifiers, Representational Similarity Analysis, and model ablations), we investigate how fine-tuning affects the representations of the BERT model. We find that while fine-tuning necessarily makes significant changes, it does not lead to catastrophic forgetting of linguistic phenomena. We instead find that fine-tuning primarily affects the top layers of BERT, but with noteworthy variation across tasks. In particular, dependency parsing reconfigures most of the model, whereas SQuAD and MNLI appear to involve much shallower processing. Finally, we also find that fine-tuning has a weaker effect on representations of out-of-domain sentences, suggesting room for improvement in model generalization.