Cow behaviour is a major factor influencing dairy herd profitability and is an indicator of animal welfare and disease. Behaviour is a complex network of behavioural patterns in response to environmental and social stimuli and human handling. Advances in agricultural technology have led to changes in dairy cow husbandry systems worldwide. Increasing herd sizes, less time availability to take care of the animals and modern technology such as automatic milking systems (AMSs) imply limited human-cow interactions. On the other hand, cow behaviour responses to the technical environment (cow-AMS interactions) simultaneously improve production efficiency and welfare and contribute to simplified "cow handling" and reduced labour time. Automatic milking systems generate objective behaviour traits linked to workability, milkability and health, which can be implemented into genomic selection tools. However, there is insufficient understanding of the genetic mechanisms influencing cow learning and social behaviour, in turn affecting herd management, productivity and welfare. Moreover, physiological and molecular biomarkers such as heart rate, neurotransmitters and hormones might be useful indicators and predictors of cow behaviour. This review gives an overview of published behaviour studies in dairy cows in the context of genetics and genomics and discusses possibilities for breeding approaches to achieve desired behaviour in a technical production environment.