Accumulating behavioral and neurophysiological studies support the idea of infantile (cute) faces as highly biologically relevant stimuli rapidly and unconsciously capturing attention and eliciting positive/affectionate behaviors, including willingness to care. It has been hypothesized that the presence of infantile physical and behavioral features in companion (or pet) animals (i.e. dogs and cats) might form the basis of our attraction to these species. Preliminary evidence has indeed shown that the human attentional bias toward the baby schema may extend to animal facial configurations. In this review, the role of facial cues, specifically of infantile traits and facial signals (i.e. eyes gaze) as emotional and communicative signals is highlighted and discussed as regulating human-animal bond, similarly to what can be observed in the adult-infant interaction context. Particular emphasis is given to the neuroendocrine regulation of social bond between humans and animals through oxytocin secretion. Instead of considering companion animals as mere baby substitutes for their owners, in this review we highlight the central role of cats and dogs in human lives. Specifically, we consider the ability of companion animals to bond with humans as fulfilling the need for attention and emotional intimacy, thus serving similar psychological and adaptive functions as human-human friendships. In this context, facial cuteness is viewed not just as a releaser of care/parental behavior, but more in general as a trait motivating social engagement. To conclude, the impact of this information for applied disciplines is briefly described, particularly in consideration of the increasing evidence of the beneficial effects of contacts with animals for human health and wellbeing.