Mutation plays the primary role in evolution that Weismann mistakenly attributed to sex. Homologous recombination, as in sex, is important for population genetics--shuffling of minor variants, but relatively insignificant for large-scale evolution. Major evolutionary innovations depend much more on illegitimate recombination, which makes novel genes by gene duplication and by gene chimaerisation--essentially mutational forces. The machinery of recombination and sex evolved in two distinct bouts of quantum evolution separated by nearly 3 Gy of stasis; I discuss their nature and causes. The dominant selective force in the evolution of recombination and sex has been selection for replicational fidelity and viability; without the recombination machinery, accurate reproduction, stasis, resistance to radical deleterious evolutionary change and preservation of evolutionary innovations would be impossible. Recombination proteins betray in their phylogeny and domain structure a key role for gene duplication and chimaerisation in their own origin. They arose about 3.8 Gy ago to enable faithful replication and segregation of the first circular DNA genomes in precellular ancestors of Gram-negative eubacteria. Then they were recruited and modified by selfish genetic parasites (viruses; transposons) to help them spread from host to host. Bacteria differ fundamentally from eukaryotes in that gene transfer between cells, whether incidental to their absorptive feeding on DNA and virus infection or directly by plasmids, involves only genomic fragments. This was radically changed by the neomuran revolution about 850 million years ago when a posibacterium evolved into the thermophilic cenancestor of eukaryotes and archaebacteria (jointly called neomurans), radically modifying or substituting its DNA-handling enzymes (those responsible for transcription as well as for replication, repair and recombination) as a coadaptive consequence of the origin of core histones to stabilise its chromosome. Substitution of glycoprotein for peptidoglycan walls in the neomuran ancestor and the evolution of an endoskeleton and endomembrane system in eukaryotes alone required the origin of nuclei, mitosis and novel cell cycle controls and enabled them to evolve cell fusion and thereby the combination of whole genomes from different cells. Meiosis evolved because of resulting selection for periodic ploidy reduction, with incidental consequences for intrapopulation genetic exchange. Little modification was needed to recombination enzymes or to the ancient bacterial catalysts of homology search by spontaneous base pairing to mediate chromosome pairing. The key innovation was the origin of meiotic cohesins delaying centromere splitting to allow two successive divisions before reversion to vegetative growth and replication, necessarily yielding two-step meiosis. Also significant was the evolution of synaptonemal complexes to stabilise bivalents and of monopolins to orient sister centromeres to one spindle pole. The primary significance of sex was not to promote evolutionary change but to limit it by facilitating ploidy cycles to balance the conflicting selective forces acting on rapidly growing phagotrophic protozoa and starved dormant cysts subject to radiation and other damage.