Changing someone's opinion is arguably one of the most important challenges of social interaction. The underlying process proves difficult to study: it is hard to know how someone's opinions are formed and whether and how someone's views shift. Fortunately, ChangeMyView, an active community on Reddit, provides a platform where users present their own opinions and reasoning, invite others to contest them, and acknowledge when the ensuing discussions change their original views. In this work, we study these interactions to understand the mechanisms behind persuasion. We find that persuasive arguments are characterized by interesting patterns of interaction dynamics, such as participant entry-order and degree of back-and-forth exchange. Furthermore, by comparing similar counterarguments to the same opinion, we show that language factors play an essential role. In particular, the interplay between the language of the opinion holder and that of the counterargument provides highly predictive cues of persuasiveness. Finally, since even in this favorable setting people may not be persuaded, we investigate the problem of determining whether someone's opinion is susceptible to being changed at all. For this more difficult task, we show that stylistic choices in how the opinion is expressed carry predictive power.