We present a computational framework for understanding the social aspects of emotions in Twitter conversations. Using unannotated data and semisupervised machine learning, we look at emotional transitions, emotional influences among the conversation partners, and patterns in the overall emotional exchanges. We find that conversational partners usually express the same emotion, which we name Emotion accommodation, but when they do not, one of the conversational partners tends to respond with a positive emotion. We also show that tweets containing sympathy, apology, and complaint are significant emotion influencers. We verify the emotion classification part of our framework by a human-annotated corpus.