Wolves, dogs and humans share extremely social and cooperative minds. These similarities are rooted in phylogenetic homology and in the convergence of neuronal and physiological mechanisms, particularly the brain, in the functioning and communication of basic affects and in the mechanisms of stress and calming. The domesticated wolves called dogs are particularly close companion animals. Both Palaeolithic humans and wolves were hypercursorial hunters, cooperating in complex and prosocial ways within their clans with respect to hunting, raising offspring, and defending against conspecific and heterospecific competitors and predators. These eco-social parallels have shaped the development of similar social mindsets in wolves and humans. Over the millennia of domestication, this social match was fine-tuned, resulting in the socio-cognitive specialists humans and dogs, possessing amazingly similar social brains and minds. Therefore, it can be concluded that the quality of their relationships with their human masters is a major factor in the wellbeing, welfare and even health of dogs, as well as in the wellbeing of their human partners. Based on their strikingly similar social brains and physiologies, it can be further concluded that anthropomorphically applying human empathy to dogs in an educated manner may not be as inappropriate as previously thought.