Genre, Relevance and Global Coherence seeks to explain how discourse types or genre may influence the addressee's inferential processes in identifying the communicator's intention. There are two main areas where such an influence is often felt: the interpretation of tense and aspect markers is often said to differ in various text types, and the communication of implicatures is said to differ in various talk-exchange types. The first type of genre effects is usually approached by global coherence-based accounts whereas the second by proposals based on Gricean pragmatics. This study examines both types of accounts, arguing that the key to a solution lies in the interplay of the cognitive and communicative principles of relevance proposed by Sperber and Wilson. It unravels intricate relations between cognitive mechanisms, communicative principles and expectations of relevance in complex ostensive stimuli such as texts.