The A15 superconductor Nb3Sn has shown great promise to replace niobium as the material of choice for the construction of superconducting radio-frequency (SRF) accelerator cavities. It promises, at least on paper, greater efficiency and higher accelerating gradients, with the potential to enable the construction of smaller yet more powerful accelerators than can be constructed using niobium. Although the state-of-the-art performance of cavities coated with Nb3Sn has shown great potential, the achievable limits in cavity quality factor Q0 and accelerating gradient Eacc are still below that expected given theoretical limits. In this work we present and discuss results of experiments carried out to understand the current limitations on Q0 and Eacc, and propose methods to improve these further. We will conclude with an outlook to the future, and the prospects that Nb3Sn could enable.