One of the major claims of recent cognitive linguistics research is that metonymy constitutes a fundamental scheme of human cognition and is not just a rhetorical device employed for specific communicative purposes. The work of Klaus-Uwe Panther and others has suggested that certain metonymies are natural inference schemes operating during many aspects of language production and understanding. This chapter explores the relations between cognitive linguistic ideas on conceptual metonymy and recent psycholinguistic experiments examining online meaning construction. It is suggested that there is no direct evidence supporting the idea that conceptual metonymies are immediately recruited during metonymic language processing, but that this gap is due to the difficulties in testing whether very abstract schemes are accessed during online meaning construction. Nonetheless, there exists various experimental support for other cognitive linguistic claims about metonymy, including the importance of metonymy for highlighting certain aspects of discourse topics, the interaction of metonymy and grammatical structure in sentence comprehension, and the idea that conceptual metonymies may interact with pragmatic information to constrain specific interpretations of metonymic utterances.