Over the last years, the web witnesses a prolific growth largely due to the changing trends in the use of web technology that aims to enhance interconnectivity, self-expression and information sharing. These trends have led to the development and evolution of online social systems, but also to the creation of voluminous user-generated data. Even as these new online social media change the way we communicate, the social processes occurring remain governed by long-standing principles of human behavior and social interaction.

In this thesis, we focus on the algorithmic and computational issues involved in the study of online social interactions and processes, such as, behavior, influence and diffusion. We first present an analysis of user-generated content published online by non-technical users. Our analysis reveals cascading patterns of online communication and establishes evidence of a cascading effect occurring in online communities. Then, we design an analytical method for detecting social influence, the cause of cascading effects, in social systems. Our method suggests a strategy for studying the causality between changes of individual behavior and the social influence that individuals exert in their network. The ability of a network to carry on social processes is a characteristic that depends, to a great extent, on its topology. Therefore, slight modifications in the network topology, might have a dramatic effect on how efficiently social processes evolve. We approach network modification as a graph augmentation problem and come up with methods that can optimize connectivity properties of the network that can boost social processes. Finally, we present efficient methods that utilize information available in a user's social network in order to improve the quality of results they get back when they search the web. The main goal and premise is to re-order the list of retrieved results in a way that favors items that are more relevant to a user's interest towards a more personalized search experience.

Overall, formal understanding of principles and models of social interaction and processes that are persistent in online social media provides an opportunity to design and develop methods, algorithms and applications that can positively impact the way we interact with, search and access information online.