In transport through confined geometries with superconducting and normal leads, Andreev reflection processes can give rise to bound states (ABS). We first discuss recent transport measurements of sharp, gate-tunable ABS formed in a superconductor–quantum dot (QD)–normal system realized on an exfoliated graphene sheet. The QD is formed in graphene beneath a superconducting contact, and the ABS form when the discrete QD levels are proximity-coupled to the superconducting contact. Owing to the low density of states of graphene and the sensitivity of the QD levels to an applied gate voltage, the ABS spectra are sharp and display a striking evolution with gate voltage and bias. A theoretical analysis of this system reveals the possibility of a quantum phase transition separating phases of the QD dominated either by the proximity induced superconducting order parameter or Coulomb repulsion.