Sentiment analysis has been one of the most popular applications of natural language processing for over a decade both in academic research institutions and in industry. From a computational perspective, most current research examines the expression and extraction of opinion at two main levels of granularity: the document and the sentence. We believe that viewing opinions in a text as a simple aggregation of opinion expressions identified locally is not appropriate. We argue that discourse structure provides a crucial link between local and document levels and is needed for a better understanding of the opinions expressed in texts. Studying opinion within discourse gives rise to new challenges: What is the role of discourse relations in subjectivity analysis? What is the impact of the discourse structure in determining the overall opinion conveyed by a document? Does a discourse based approach really bring additional value compared to a classical bag of words approach? Does this additional value depend on corpus genre? In this presentation, I will attempt to answer these questions. First I will give an overview of state of the art approaches in discourse-based sentiment analysis. Then I will focus on our contributions to this field using Segmented Discourse Representation Theory (SDRT) (Asher and Lascarides, 2003) as our theoretical framework.