Many parthenogenetically reproducing animals produce offspring not clonally but through different mechanisms collectively referred to as automixis. Here, meiosis proceeds normally but is followed by the fusion of meiotic products that restores diploidy. This mechanism typically leads to a reduction in heterozygosity among the offspring compared to the mother. Following a derivation of the rate at which heterozygosity is lost at one and two loci, depending on the number of crossovers between loci and centromere, a number of models are developed to gain a better understanding of basic evolutionary processes in automictic populations. Analytical results are obtained for the expected equilibrium neutral genetic diversity, mutation-selection balance, selection with overdominance, the rate of spread of beneficial mutations, and selection on crossover rates. These results are complemented by numerical investigations elucidating how associative overdominance (two off-phase deleterious mutations at linked loci behaving like an overdominant locus) can in some cases maintain heterozygosity for prolonged times, and how clonal interference affects adaptation in automictic populations. These results suggest that although automictic populations are expected to suffer from the lack of gene shuffling with other individuals, they are nevertheless in some respects superior to both clonal and outbreeding sexual populations in the way they respond to beneficial and deleterious mutations. Implications for related genetic systems such as intratetrad mating, clonal reproduction, selfing as well as different forms of mixed sexual and automictic reproduction are discussed.