Relevance and the Conceptual Theory of Metaphor - Sperber and Wilson (2006) have recently claimed that metaphors are not a genuine cognitive phenomenon. There is a continuum, they claim, ranging from literal to figurative uses of language, and the interpretation of any sentence along that continuum can, and must, be performed by the same relevance-guided inferential procedure; therefore, metaphor interpretation would not require any special cognitive process. Following a suggestion of Gibbs and Tendahl (2006), we propose a framework according to which the relevance-theoretic account has to be integrated with the conceptual theory of metaphors. In particular, we will suggest that the relevance-guided inferential procedure has to be sensitive not only to the balance between cognitive efforts and effects, but also to the nature of the conceptual relations between context and verbal meanings; in the case of metaphor comprehension, this amounts to saying that sensitivity to conceptual mappings is part of how the procedure works, at least for fresh metaphors. As a consequence, there is a clear sense in which metaphor is, after all, a specific cognitive phenomenon. Keywords: Conceptual theory, Figurative meaning, Literal meaning, Mapping, Metaphor, Relevance.