Internet memes have been studied widely for their role in establishing and maintaining social relationships, and shaping public opinion, online. However, they are also a prominent and fast evolving multimodal genre, one which calls for an in-depth linguistic analysis. This book, the first of its kind, develops the analytical tools necessary to describe and understand contemporary 'image-plus-text' communication. It demonstrates how memes achieve meaning as multimodal artifacts, how they are governed by specific rules of composition and interpretation, and how such processes are driven by stance networks. It also defines a family of multimodal constructions in which images become structural components, while making language forms adjust to the emerging multimodal rules. Through analysis of several meme types, this approach defines the specificity of the memetic genre, describing established types, but also accounting for creative forms. In describing the 'grammar of memes', it provides a new model to approach multimodal genres.