Over the past 50 years, well over 100 twin studies have focussed on understanding factors contributing to variability in normal sleep-wake characteristics and sleep disturbances. Whilst we have gained a great deal from these studies, there is still much to be learnt. Twin studies can be used in multiple ways to answer questions beyond simply estimating heritability. This paper provides a comprehensive review of some of the most important findings from twin studies relating to sleep to date, with a focus on studies investigating genetic and environmental influences contributing to i) objective and subjective measures of normal sleep characteristics (e.g. sleep stage organisation, sleep quality); as well as sleep disturbances and disorders such as dyssomnias (e.g. insomnia, narcolepsy) and parasomnias (e.g. sleepwalking, bruxism); ii) the persistence of sleep problems from childhood to adulthood, and the possibility that the aetiological influences on sleep change with age; iii) the associations between sleep disturbances, emotional, behavioural and health-related problems; and iv) processes of gene-environment correlation and interaction. We highlight avenues for further research, emphasising the need to further consider the aetiology of longitudinal associations between sleep disturbances and psychopathology; the genetic and environmental overlap between sleep and numerous phenotypes; and processes of gene-environment interplay and epigenetics.