Ontic structuralism or ontic structural realism in the philosophy of physics can be broadly considered as an interpretative strategy providing a set of conceptual and metaphysical tools—or, more ambitiously, an ontological framework—in order to account for central features of current fundamental physics. This article aims to review the main structuralist interpretative moves in the context of our two best fundamental physical theories of matter and spacetime, namely, quantum theory (quantum mechanics and quantum field theory) and general relativity. We highlight in particular the structuralist understanding of permutation invariance, entanglement and nonlocality in quantum theory, and of the dynamical features of spacetime, (gauge-theoretic...