Intralocus sexual conflict occurs when selection on a shared trait in one sex displaces the other sex from its phenotypic optimum. It arises because many shared traits have a common genetic basis but undergo contrasting selection in the sexes. A recent surge of interest in this evolutionary tug of war has yielded evidence of such conflicts in laboratory and natural populations. Here we highlight outstanding questions about the causes and consequences of intralocus sexual conflict at the genomic level, and its long-term implications for sexual coevolution. Whereas recent thinking has focussed on the role of intralocus sexual conflict as a brake on sexual coevolution, we urge a broader appraisal that also takes account of its potential to drive adaptive evolution and speciation.