A theoretical framework developed by George Lakoff and Mark Johnson, but also associated with other influential scholars including Zoltán Kövecses, Raymond Gibbs, Eve Sweetser and Mark Turner. Conceptual Metaphor Theory was first presented by Lakoff and Johnson in their 1980 volume Metaphors We Live By. Conceptual Metaphor Theory was one of the earliest theoretical frameworks to be developed in cognitive semantics and provided much of the early theoretical impetus for this approach to the relationship between language, mind and embodied experience. The basic premise of conceptual metaphor theory is that metaphor is not simply a stylistic feature of language but that thought itself is fundamentally metaphorical in nature. According to this view, conceptual structure is organised by cross-domain mappings or correspondences between conceptual domains. Some of these mappings are due to pre-conceptual embodied experiences while others build on these experiences in order to form more complex conceptual structures. For instance, we can think and talk about the concept of quantity in terms of the concept of vertical elevation, as in She got a really high mark in the test, where high relates not literally to physical height but to a good mark. According to conceptual metaphor theory, this is because the conceptual domain (2) quantity is conventionally structured and therefore understood in terms of the conceptual domain vertical elevation.

Conceptual operations involving mappings, such as conceptual metaphor, are known more generally as conceptual projection.