This thesis deals with the analysis of interpersonal communication dynamics in online social networks and social media. Our central hypothesis is that communication dynamics between individuals manifest themselves via three key aspects: the information that is the content of communication, the social engagement i.e. the sociological framework emergent of the communication process, and the channel i.e. the media via which communication takes place. Communication dynamics have been of interest to researchers from multi-faceted domains over the past several decades. However, today we are faced with several modern capabilities encompassing a host of social media websites. These sites feature variegated interactional affordances, ranging from blogging, micro-blogging, sharing media elements as well as a rich set of social actions such as tagging, voting, commenting and so on. Consequently, these communication tools have begun to redefine the ways in which we exchange information, our modes of social engagement, and mechanisms of how the media characteristics impact our interactional behavior. The outcomes of this research are manifold. We present our contributions in three parts, corresponding to the three key organizing ideas. First, we have observed that user context is key to characterizing communication between a pair of individuals. However interestingly, the probability of future communication seems to be more sensitive to the context compared to the delay, which appears to be rather habitual. Further, we observe that diffusion of social actions in a network can be indicative of future information cascades; that might be attributed to social influence or homophily depending on the nature of the social action. Second, we have observed that different modes of social engagement lead to evolution of groups that have considerable predictive capability in characterizing external-world temporal occurrences, such as stock market dynamics as well as collective political sentiments. Finally, characterization of communication on rich media sites have shown that conversations that are deemed "interesting" appear to have consequential impact on the properties of the social network they are associated with: in terms of degree of participation of the individuals in future conversations, thematic diffusion as well as emergent cohesiveness in activity among the concerned participants in the network. Based on all these outcomes, we believe that this research can make significant contribution into a better understanding of how we communicate online and how it is redefining our collective sociological behavior.