Recent experiments on two-dimensional moiré materials have uncovered fractional quantum anomalous Hall states at zero magnetic field, accompanied by superconductivity in their vicinity, both in twisted MoTe₂ and in rhombohedral multilayer graphene. Because doping a fractional Chern insulator naturally liberates itinerant anyons, these superconductors are natural candidates for the long-sought anyon superconductor first envisioned by Laughlin. Yet the standard picture runs into trouble: near the 2/3 filling fractional Chern insulator in twisted MoTe₂, the elementary excitation is a charge-e/3 anyon whose exchange statistics lie outside Laughlin's anyon statistics sequence, forcing existing theories to assume that anyons first bind into composite objects. In this talk I will present a different approach that works directly with the minimally charged anyons and requires no additional pairing interaction: the anyon statistics itself supplies the glue. This route reveals a hidden weak-pairing superconducting phase, physically distinct from the conventional strong-pairing state reached by pre-binding anyons. The distinction is sharp and measurable. Whereas previous theories predict a chiral central charge inconsistent with numerics, the weak-pairing phase carries c₋ = −1/2, in agreement with recent calculations, and yields a quantized thermal Hall response as a direct experimental signature. The framework also admits controlled weak- and strong-coupling limits, recovering Laughlin's theory in the latter, and generalizes to a family of new chiral superconductors near other fractional fillings. In the final part of the talk, I will turn to rhombohedral pentalayer graphene and discuss the interplay between crystallization, fractional quantum Hall states and superconductivity. Together these results suggest that the superconductors emerging near fractional Chern insulators may be richer than the original anyon-superconductor paradigm anticipated, with concrete predictions that experiments can now test.