Psychosocial stress may impair immune functions and provoke the development of pathologies. The underlying communication between the brain and the immune system is being studied predominantly in rodents. However, pigs offer several advantages as preclinical models for humans because pigs are more similar to humans than rodents in many anatomical and physiological characteristics. Unlike in rodents, the main stress-induced glucocorticoid in humans and pigs is cortisol with a similar circadian rhythm. In this study, we summarize data on short-term and long-term effects of social stress in pigs for their immunity and neuroendocrine regulation with consequences for their health and well-being. As typical social stressors, regrouping, crowding, social isolation, and maternal deprivation have been studied. Psychosocial stress in pigs may affect various reactions of innate and adaptive immunity, such as leukocyte distribution, cytokine secretion, lymphocyte proliferation, and antibody production as well as immune responses to viral infection or vaccination. Furthermore, social stress may induce or promote gastrointestinal diseases through dysregulation of inflammatory processes. In piglets, psychosocial stress may also result in glucocorticoid resistance of lymphocytes, which has been discussed as a cause of allergic asthma in humans. Stress-related neuroendocrine alterations in the cortico-limbic structures, such as the prefrontal cortex, amygdala, hippocampus and hypothalamus, have been demonstrated in pigs at different ages. Based on these data, we propose using pigs as models for psychosocial stress in humans to study the mechanisms of brain-to-immune and immune-to-brain communication from the systemic level down to the cellular and subcellular levels.