Despite the increasing centrality of Internet memes for everyday political circulations and practices, their emergent implications as low-cultural artefacts of global politics have received little theoretical attention. In this article, I develop a critical theory of memes to provide a conceptual apparatus to understand the global political implications and possibilities of this pop-cultural phenomenon. I argue that, in order to attend to the emergent implications of memes and consider their differentiations from other pop-cultural phenomena, we need to unpack the spatial logic through which memes emerge and circulate. Analysing this spatial logic through the concept of the ‘memescape’ and deploying Gilles Deleuze and Felix Guattari’s notions of striated and smooth spaces, this article articulates the spatial logic of the memescape as comprising rhizomatic, decentralised circulations of digital content; nomadic, playful, and humorous disruptions of once-stable signs; and affective congregations of a multiplicity of subjects. Through two examples exploring how these smooth spatial tendencies produce divergent political potentials in the resistant memes of Indigenous digital communities and reactionary memes of the Alt-Right, I conclude that the global politics of the memescape is open-ended and undetermined which requires careful and nuanced political and ethical attention to actualise its futures for emancipatory horizons.