Proton radiotherapy is undergoing rapid expansion both within the UK and internationally, but significant challenges still need to be overcome if maximum benefit is to be realised from this technique. One major limitation is the persistent uncertainty in proton relative biological effectiveness (RBE). While RBE values are needed to link proton radiotherapy to our existing experience with photon radiotherapy, RBE remains poorly understood and is typically incorporated as a constant dose scaling factor of 1.1 in clinical plans. This is in contrast to extensive experimental evidence indicating that RBE is a function of dose, tissue type, and proton linear energy transfer, among other parameters. In this article, we discuss the challenges associated with obtaining clinically relevant values for proton RBE through commonly-used assays, and highlight the wide range of other experimental end points which can inform our understanding of RBE. We propose that accurate and robust optimization of proton radiotherapy ultimately requires a multiscale understanding of RBE, integrating subcellular, cellular, and patient-level processes.