In the vast majority of sexual life cycles, fusion between single-celled gametes is directly followed by nuclear fusion, leading to a diploid zygote and a lifelong commitment between two haploid genomes. Mushroom-forming basidiomycetes differ in two key respects. First, the multicellular haploid mating partners are fertilized in their entirety, each cell being a gamete that simultaneously can behave as a female, i.e. contributing the cytoplasm to a zygote by accepting nuclei, and a male gamete, i.e. only donating nuclei to the zygote. Second, after gamete union, the two haploid genomes remain separate so that the main vegetative stage, the dikaryon, has two haploid nuclei per cell. Only when the dikaryon produces mushrooms, do the nuclei fuse to enter a short diploid stage, immediately followed by meiosis and haploid spore formation. So in basidiomycetes, gamete fusion and genome mixing (sex) are separated in time. The ‘living apart together’ of nuclei in the dikaryon maintains some autonomy for nuclei to engage in a relationship with a different nucleus. We show that competition among the two nuclei of the dikaryon for such ‘extramarital affairs’ may lead to genomic conflict by favouring genes beneficial at the level of the nucleus, but deleterious at that of the dikaryon.This article is part of the themed issue ‘Weird sex: the underappreciated diversity of sexual reproduction’.