Despite decades of research, we do not have a satisfactory concurrency semantics for any general-purpose programming language that aims to support concurrent systems code. The Java Memory Model has been shown to be unsound with respect to standard compiler optimisations, while the C/C++11 model is too weak, admitting undesirable thin-air executions. Our goal in this paper is to articulate this major open problem as clearly as is currently possible, showing how it arises from the combination of multiprocessor relaxed-memory behaviour and the desire to accommodate current compiler optimisations. We make several novel contributions that each shed some light on the problem, constraining the possible solutions and identifying new difficulties.