Topological phases of matter are defined by their nontrivial ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. In this talk, I will discuss a peculiar variety of symmetry-protected topological phases (SPTs), dubbed “fragile topological insulators,” which feature symmetry-protected quantum entanglement but lack the usual sense of robustness commonly assumed for SPTs. More specifically, the protected entanglement in a fragile topological insulator can be dissolved simply by the addition of entanglement-free degrees of freedom. We will first provide an example of fragile topology among non-interacting electrons, and then discuss its stability against the introduction of interactions. Time permitting, I will also make connection to the physics of magic-angle twisted bilayer graphene.