Odonates (dragonflies) are well known for the ability of the males to displace sperm stored in the female's sperm-storage organs during copulation. By this means, copulating males are able to increase their fertilization success. This ability has been used as an example to illustrate a conflict of interests between the sexes in which males have evolved sperm-displacement mechanisms whilst females have presumably evolved means to avoid sperm displacement. The present review has four aims: (1) to describe the copulatory mechanisms used during sperm displacement; (2) to analyse the causes of sperm usage patterns; (3) to discuss this information using current hypotheses on conflict between the sexes; and (4) to illuminate topics for further research. Four copulatory mechanisms are described: sperm removal (physical withdrawal of stored sperm), sperm repositioning (‘pushing’ of rival sperm to sites where its use will be least likely), female sensory stimulation to induce sperm ejection, and sperm flushing (displacement of sperm using the copulating male's sperm). Sperm-precedence studies in Odonata are scarce and their values vary considerably between species. In those species in which sperm displacement is incomplete, the last copulating male obtains a high but variable short-term fertilization success which decreases with time. Some male and female factors affecting sperm precedence patterns are mentioned: (1) male variation in genital morphology; (2) duration of copulation influenced by the male (the longer the copulation, the more stored sperm displaced); (3) adaptations of the sperm-storage organs that allow the female to manipulate the sperm she has received (i.e. avoiding sperm displacement, re-distributing sperm masses, favouring sperm located in certain sites and ejecting sperm after copulation). We suggest that male and female odonates have co-evolved at the level of genital function with the control of stored sperm as the focus of the conflict. The benefits for males in this co-evolution lie in maximizing their fertilization success. However, it is not clear what females obtain from storing sperm and making it unreachable during sperm displacement. Two hypothetical benefits that females may obtain for which some evidence has been gathered are genetic diversity and viability genes. It is finally suggested that odonates can become excellent subjects of study for testing current ideas related to sexual conflict and speciation processes through sexual selection.