Superconductivity and the fractional quantum Hall (FQH) effect are two landmark discoveries of modern physics. While superconductivity requires the presence of an effective pairing glue, the FQH effect typically emerges due to strong repulsion among electrons. Nevertheless, experiments in two-dimensional materials have recently observed both phases in close proximity. A particularly tantalizing explanation for this interplay is Laughlin's idea of “anyon superconductivity”, which proposes that superconductivity arises from a finite density of anyons — exotic quasiparticles emerging from the FQH state — carrying fractional charge. I will demonstrate that anyon superconductivity can naturally emerge from an unconventional energy hierarchy of excitations when the system is close to a topological phase transition. These insights may help guide future experiments and develop theories for continuous transitions between FQH states and chiral superconductors. If time permits, I will present numerical results on microscopic models that are loosely related to recent experiments and show the emergence of superconductivity near the quantum Hall regime.