DescriptionHuman communication often involves the use of figurative language, such as verbal irony or sarcasm, where the speakers usually mean the opposite of what they say. In this dissertation, I address three problems regarding verbal irony: automatic identification of verbal irony and its characteristics from social media platforms, interpretation of verbal irony, and examining the role of verbal irony in identifying dis(agreement) relations in discussion forums. To automatically detect verbal irony I propose computational models that are based on theoretical underpinnings of irony. I first reframe the question of irony identification as a word-sense disambiguation problem to understand how particular target words are used in the literal or figurative sense. Next, I thoroughly analyze two characteristics of irony; irony markers, and irony factors. I propose empirical models to identify irony, irrespective of contextual knowledge as well as with conversation context. I also analyze the context to understand what triggers an ironic reply and perform user studies to explain the machine learning model predictions. Regarding the interpretation of irony, I offer a typology of linguistic strategies for verbal irony interpretation and link it to various theoretical linguistic frameworks. I design computational models to capture these strategies and present empirical studies aimed to answer two questions: (1) what is the distribution of linguistic strategies used by hearers to interpret ironic messages; (2) do hearers adopt similar strategies for interpreting the speaker's ironic intent? Finally, I turn to the application of irony to show how the use of irony-based features assists in identifying argumentative relations from discussion forums. I perform this research on two types of social media datasets: self-labeled data (e.g., microblogging platforms such as Twitter and Reddit threads), and crowdsource-labeled corpus (e.g., Internet Argumentative Corpus).