The human–animal relationship is ancient, complex and multifaceted. It may have either positive effects on humans and animals or poor or even negative and detrimental effects on animals or both humans and animals. A large body of literature has investigated the beneficial effects of this relationship in which both human and animals appear to gain physical and psychological benefits from living together in a reciprocated interaction. However, analyzing the literature with a different perspective it clearly emerges that not rarely are human–animal relationships characterized by different forms and levels of discomfort and suffering for animals and, in some cases, also for people. The negative physical and psychological consequences on animals’ well-being may be very nuanced and concealed, but there are situations in which the negative consequences are clear and striking, as in the case of animal violence, abuse or neglect. Empathy, attachment and anthropomorphism are human psychological mechanisms that are considered relevant for positive and healthy relationships with animals, but when dysfunctional or pathological determine physical or psychological suffering, or both, in animals as occurs in animal hoarding. The current work reviews some of the literature on the multifaceted nature of the human–animal relationship; describes the key role of empathy, attachment and anthropomorphism in human–animal relationships; seeks to depict how these psychological processes are distorted and dysfunctional in animal hoarding, with highly detrimental effects on both animal and human well-being.