Interpreters regularly have to make real time decisions about word or sentence meaning in the original text before they can select their best equivalents in the target language. In some situations, the context (linguistic or situational) may help to disambiguate the problematic item. Establishing the fastest way to arrive at the optimal meaning is a crucial skill for interpreters who work without previous knowledge of texts to be translated (as is the case for most conference or court interpreters). Relevance Theory, as formulated by Sperber and Willson (1986/1995) offers insights into two aspects of messages that need to be understood in communication: explicatures and implicatures. While implicatures may seem more problematic to resolve in real life situations, explicatures often pose significant difficulty in translation. This chapter uses examples from court interpretation to discuss both types of interpretation problems and what practical tools Relevance Theory can offer to assist interpreters to solve them.