Scientific research on factors causing the reduction of well-being in sheep and goats is rather recent, as are studies of strategies to minimize the adverse effects of environmental challenges and improper management practices on flock welfare. Sheep and goats, considered very rustic animals, are reared prevalently under extensive production systems and are widespread mainly in marginal areas. For these reasons, only few studies on the welfare of these species have been carried out in the past. More recently, the scenario has changed, due to a gradual diffusion of intensive and semi-intensive production systems, especially in dairy sheep and goat breeds, to the growing concern of consumers about the life conditions of farmed animals, and to the issuing of a number of rules and laws on the safety of animal products and well-being of farmed livestock. As a consequence, several research groups have turned their attention to the welfare of sheep and goats. Nevertheless, information on this topic is still scarce. This paper reviews major critical points regarding the endangerment of welfare in farmed sheep and goats. Climatic extremes and seasonal fluctuations in herbage amount and quality are discussed as important causes of the reduction of well-being in extensive production systems, which can impair production efficiency of grazing animals and dramatically affect the welfare and health status of sheep and goats. Space allowance and structures of sheep and goat houses are described as the main potential sources of discomfort for housed flocks, together with inadequate control of micro-environment, and inappropriate milking procedures and human-animal interactions. Recent studies on the impact of high ambient temperature, different ventilation regimes, high stocking densities, reduced airspace and poor litter management on behaviour, immune and endocrine response, and on performance of sheep and goats are discussed. The effects of inadequate milking procedures and improper milking technical parameters on welfare and udder health of sheep and goats are also discussed. Finally, some practices aimed at minimizing emotional and nutritional stresses of lambs and kids after early separation from the mother, before the transition to artificial rearing, and at weaning time are described.