AI systems are being deployed to support human decision making in high-stakes domains. In many cases, the human and AI form a team, in which the human makes decisions after reviewing the AI's inferences. A successful partnership requires that the human develops insights into the performance of the AI system, including its failures. We study the influence of updates to an AI system in this setting. While updates can increase the AI's predictive performance, they may also lead to changes that are at odds with the user's prior experiences and confidence in the AI's inferences, hurting therefore the overall team performance. We introduce the notion of the compatibility of an AI update with prior user experience and present methods for studying the role of compatibility in human-AI teams. Empirical results on three high-stakes domains show that current machine learning algorithms do not produce compatible updates. We propose a re-training objective to improve the compatibility of an update by penalizing new errors. The objective offers full leverage of the performance/compatibility tradeoff, enabling more compatible yet accurate updates.