In the richer and more advanced societies, the preoccupation of the consumers by the welfare of our farm animals is gradually increasing. In the present article the possibilities of genetic improvement of the animal welfare are reviewed. We begin defining animal welfare and which are the factors that determine it, relating welfare and temperament and the ability to cope with stress. The description of the psycho‑biological aspects of these phenomena precedes the discussion of methodological difficulties in measuring them and the methodology of genetic analysis. The knowledge relative to the behaviour and the capacity of adaptation are exemplified in three types of livestock: dairy cows, beef cattle and sheep reared in extensive conditions. The differences between breeds and individuals of the same breed, the consequences on the welfare of an intense application of artificial selection, and the different strategies to cope with environmental challenges are shown; on the basis of these phenomena, possible alternatives of improvement are discussed. Finally it is postulated the necessity to continue investigating the genetic aspects of stress and welfare, as well as their relationships with production traits, in spite of the difficulties that these investigations involve.