The idea that sex functions to provide variation for natural selection to act upon was first advocated by August Weismann and it has dominated much discussion on the evolution of sex and recombination since then. The goal of this paper is to further extend this hypothesis and to assess its place in a larger body of theory on the evolution of sex and recombination. A simple generic model is developed to show how fitness variation and covariation interact with selection for recombination and illustrate some important implications of the hypothesis: (1) the advantage of sex and recombination can accrue both to reproductively isolated populations and to modifiers segregating within populations, but the former will be much larger than the latter; (2) forces of degradation that are correlated across loci within an individual can reduce or reverse selection for increased recombination; and (3) crossing-over (which can occur at different places in different meioses) will create more variability than having multiple chromosomes and so will have more influence on the efficacy of selection. Several long-term selection experiments support Weismann's hypothesis, including those showing a greater response to selection in populations with higher rates of recombination and higher rates of recombination evolving as a correlated response to selection for some other character. Weismann's hypothesis is also consistent with the sporadic distribution of obligate asexuality, which indicates that clones have a higher rate of extinction than sexuals. Weismann's hypothesis is then discussed in light of other patterns in the distribution of sexuality versus asexuality. To account for variation in the frequency of obligate asexuality in different taxa, a simple model is developed in which this frequency is a function of three parameters: the rate of clonal origin, the initial fitness of clones when they arise, and the rate at which that fitness declines over time. Variation in all three parameters is likely to be important in explaining the distribution of obligate asexuality. Facultative asexuality also exists, and for this to be stable it seems there must be ecological differences between the sexual and asexual propagules as well as genetic differences. Finally, the timing of sex in cyclical parthenogens is most likely set to minimize the opportunity costs of sex. None of these patterns contradict Weismann's hypothesis, but they do show that many additional principles unrelated to the function of sex are required to fully explain its distribution. Weismann's hypothesis is also consistent with what we know about the mechanics and molecular genetics of recombination, in particular the tendency for chromatids to recombine with a homolog rather than a sister chromatid at meiosis, which is opposite to what they do during mitosis. However, molecular genetic studies have shown that cis-acting sites at which recombination is initiated are lost by gene conversion as a result, a factor that can be expected to affect many fine details in the evolution of recombination. In summary, although Weismann's hypothesis must be considered the leading candidate for the function of sex and recombination, nevertheless, many additional principles are needed to fully account for their evolution.