Title:  *Quantum Vortices of Photons* Abstract:  We explore the topological structures that emerge in the wavefunction of strongly interacting photons inside a quantum nonlinear optical medium. In our experiments, photons acquire strong effective interactions by mapping them onto Rydberg polaritons in ultracold atoms. These interactions imprint a spatially varying phase, giving rise to quantum vortices – phase singularities in the few-photon wavefunction – and to extended structures such as vortex lines and rings [Science 381, 193-198 (2023)]. The vortex rings are warped by the underlying dispersion [arXiv:2502.11553 (2025)], and the enclosed phase flip offers a resource for deterministic quantum logic. Going beyond co-propagating photons, we find that counter-propagating configurations exhibit longer-range and richer vortex interactions, opening new directions for quantum nonlinear optics [arXiv:2506.01124 (2025)].