In this chapter we argue that metaphorical utterances often contain source-domain elements that are important for the overall meaning of the utterance but that should not themselves be given a parallel in (be mapped into) the target domain, either because it is difficult to do so or because doing so is not important for linking the utterance into the context supplied by the discourse. Non-parallelism goes hand-in-hand with metaphor understanding processes that are strongly guided by context. The chapter discusses various ways in which understanding might be guided by context. A particularly strong form of context-guided understanding is context-driven understanding, a form of which is used in an AI approach to metaphor understanding that the author and colleagues have developed. (John Barnden)