Twitter and other social media platforms are increasingly used as the primary way in which people speak with each other. As opposed to other platforms, Twitter is interesting in that many of these dialogues are public and so we can get a view into the dynamics of dialogues and how they differ from other other tweet behaviors. We here analyze tweets gathered from 2400 twitter streams over a one month period. We study social interactions in three important dimensions: what are the salient user behaviors in terms of how often they have social interactions and how these interactions are spread among different people; what are the characteristics of the dialogues, or sets of tweets, that we can extract from these interactions, and what are the characteristics of the social network which emerges from considering these interactions? We find that roughly half of the users spend a fair amount of time interacting whereas 40% of users do not seem to have active interactions. We also find that the vast majority of active dialogues only involve two people despite the public nature of these tweets. We finally find that while the emerging social network does contain a giant component, the component clearly is a set of well-defined tight clusters which are loosely connected.