Recent activities in virtually all fields engaged in consciousness studies indicate early signs of a structural turn, where verbal descriptions or simple formalizations of conscious experiences are replaced by mathematical spaces and mathematical structures. My goal in this talk is to offer a very preliminary account of what a structural turn might imply for theories of consciousness: which opportunities arise, what challenges we might have to face, and how structural theories of consciousness might impact the development of consciousness science at large. I will also address the fundamental question of what it means to represent consciousness mathematically in the first place and provide a quick overview of how GNWT can be structuralized. My hope is that the presentation sparks discussion and further thoughts in the audience from whom I can learn as well.