We study patterns of behavior in bilateral bargaining situations using a rich new data set describing back-and-forth sequential bargaining occurring in over 25 million listings from eBay's Best Offer platform. We compare observed behavior to predictions from the large theoretical bargaining literature. One-third of bargaining interactions end in immediate agreement, as predicted by complete-information models. The majority of sequences play out differently, ending in disagreement or delayed agreement, which have been rationalized by incomplete information models. We find that stronger bargaining power and better outside options improve agents' outcomes. Robust empirical findings that existing models cannot rationalize include reciprocal (and gradual) concession behavior and delayed disagreement. Another robust pattern at odds with existing theory is that players exhibit a preference for making and accepting offers that split the difference between the two most recent offers. These observations suggest that behavioral norms, which are neither incorporated nor explained by existing theories, play an important role in the success of bargaining outcomes.