The conceptual-mapping approach to metaphor, which views its essence as consisting of deeply embedded cognitive structures that recruit elements of repeating patterns in physical and sensory experience to render abstract concepts easier to comprehend, has been the dominant paradigm of metaphor scholarship for the past four decades. This chapter begins by summarising the key points of conceptual metaphor theory (CMT) and identifying its main points of correspondence with, and divergence from, the interactionist view of metaphor introduced in Chap. 2. The application of this framework to comics focuses on non-mimetic drawing devices that are used to organise individual depictions into temporally and causally related sequences, and to represent non-visible affective and introspective experiences. Analysis of the first group applies conceptual metaphors that guide our perception of time and construal of events to the analysis of panelisation in comics. In the second group, conceptual metaphors that characterise the experience of emotion and the nature of cognition are applied to the analysis of pictorial runes and the contents of thought balloons. The main argument running through the chapter is that the highlighted drawing devices operate as graphic reifications of cognitive processes identified by theories of embodied cognition.