Mate choice for good-genes remains one of the most controversial evolutionary processes ever proposed. This is partly because strong directional choice should theoretically deplete the genetic variation that explains the evolution of this type of female mating preference (the socalled lek paradox). Moreover, good-genes benefits are generally assumed to be too small to outweigh opposing direct selection on females. Here, we review recent progress in the study of mate choice for genetic quality, focussing particularly on the potential for genotype by environment interactions (GEIs) to rescue additive genetic variation for quality, and thereby resolve the lek paradox. We raise five questions that we think will stimulate empirical progress in this field, and suggest directions for research in each area: ( 1) How is condition-dependence affected by environmental variation? ( 2) How important are GEIs for maintaining additive genetic variance in condition? ( 3) How much do GEIs reduce the signalling value of male condition? ( 4) How does GEI affect the multivariate version of the lek paradox? ( 5) Have mating biases for high-condition males evolved because of indirect benefits?.