Artificial weaning is the separation of the mother and her lamb, involving the forced ending of suckling and milk supply by the ewes to their lambs. Artificial weaning time varies depending on the purpose of each sheep farm and the characteristics of the lambs, including age and weight of the lambs, and their ability to eat solid food. Artificial weaning is performed from 24 h postpartum until around the age of natural weaning (up to 12 mo of age). Artificial weaning results in the breaking of the ewe-lamb bond, the end of suckling and the complete replacement of milk by solid food, frequently added to changes in both the physical and social environment. It triggers behavioural, physiological and immunological changes that generate negative consequences on the health of both ewes and lambs, as well as on the growth of the lambs, rising animal welfare concerns. As artificial weaning is considered one of the most stressful situations in the life of farm mammals, it is important to consider the factors involved in those responses to develop adequate strategies and improve sheep welfare at weaning. The most frequently used method is the abrupt separation of the ewes and their lambs. However, the adaptation of the animals after weaning can be improved by alternative weaning methods (e.g., progressive, two-steps weaning and mixed regimes), hormonal treatments (e.g., administration of progesterone), and pre- and postweaning management (e.g., the use of creeping feeding, and the presence of conspecifics or humans after weaning). This review presents and summarises information on the stress response and animal welfare issues at artificial weaning in sheep and some management practises that can be used to reduce these problems. The major points included are the ewe-lamb bond at birth and during the lactation period; the stress response at weaning; the factors involved in the stress response at weaning; the different types and weaning methods and their repercussions on animal welfare; and some strategies that can be used to improve sheep welfare at weaning. Lastly, we propose directions for research needed to develop practical alternatives to minimise sheep's stress response at weaning.