This dissertation is about how discourse is comprehended in real-time, and how it is represented in memory. This project begins to bridge the gap between formal linguistic theories of discourse coherence and structure and psychological theories of discourse processing. I argue that combining the insights of these two strands can bring us to a deeper understanding of the core puzzles in discourse research, e.g., what determines whether or not a sequence of clauses or sentences seems like a coherent discourse? What factors help or hinder the on-line comprehension, the incremental interpretation, of discourse? How is discourse structured in memory, and to what degree does this structure resemble formal linguistic representations of discourse? I approach these questions via three sets of experiments. First, I investigate the role of temporal information in on-line discourse comprehension, give special scrutiny to the common assumption that progression is the default temporal relation in discourse processing. My results suggest that, if progression is any sort of default, it is not the sort that has a strong influence on on-line processing. The second set of experiments is situated in the context of Situation Model Theory, a prominent psychological theory of discourse. I investigate the roles of temporal and causal information in the construction of discourse structure in memory. Based on my findings, I argue that the influence of temporal factors may not be as clear-cut as previous work has suggested. I also argue that causal factors have a relatively large role in this domain. Finally, I turn to Segmented Discourse Representation Theory, a prominent linguistic coherence theory, and its Right Frontier Constraint, which is argued to be the primary governor of pronominal anaphora in discourse. I challenge this view, arguing that the effects that are attributed to this constraint can in fact be accounted for by independent factors that influence the salience of entities in discourse.