The interplay of correlations and molecular phonons in the superconductivity of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>A</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>60</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> fullerides

The study of alkali-doped fulleride superconductors (A3C60) challenges the conventional paradigm by exhibiting robusts-wave superconductivity within a strongly correlated Mott background. This review provides a comprehensive overview of the underlying pairing mechanism, which is fundamentally driven by the synergistic interplay between molecular Jahn-Teller phonons and Mott-Hubbard correlations. We elucidate how dynamical phonon coupling overcomes Hund's exchange to favor a low-spin ground state, while the proximity to the Mott transition selectively renormalizes the electronic kinetic energy, collectively giving rise to the optimal superconducting dome. Furthermore, we discuss the pressure-tuned evolution of these interactions and critically evaluate the recent breakthroughs and ongoing debates regarding photo-induced transient superconductivity. By unifying equilibrium correlation physics with non-equilibrium dynamics, this review highlights fullerides as a quintessential platform for exploring cooperative quantum phenomena.