Sexual reproduction is almost ubiquitous among multicellular organisms even though it entails severe fitness costs. To resolve this apparent paradox, an extensive body of research has been devoted to identifying the selective advantages of recombination that counteract these costs. Yet, how easy is it to make the transition to asexual reproduction once sexual reproduction has been established for a long time? The present review approaches this question by considering factors that impede the evolution of parthenogenesis in animals. Most importantly, eggs need a diploid chromosome set in most species in order to develop normally. Next, eggs may need to be activated by sperm, and sperm may also contribute centrioles and other paternal factors to the zygote. Depending on how diploidy is achieved mechanistically, further problems may arise in offspring that stem from 'inbreeding depression' or inappropriate sex determination systems. Finally, genomic imprinting is another well-known barrier to the evolution of asexuality in mammals. Studies on species with occasional, deficient parthenogenesis indicate that the relative importance of these constraints may vary widely. The intimate evolutionary relations between haplodiploidy and parthenogenesis as well as implications for the clade selection hypothesis of the maintenance of sexual reproduction are also discussed.