Robotic agents will be life-long companions of humans in the foreseeable future. To achieve such successful relationships, people will likely attribute emotions and personality, assign social competencies, and develop a long-lasting attachment to robots. However, without a clear theoretical framework-building on biological, psychological, and technological knowledge-current societal demands for establishing successful human-robot attachment (HRA) as a new form of inter-species interactions might fail. The study of evolutionarily adaptive animal behavior (i.e., ethology) suggests that human-animal behaviors can be considered as a plausible solution in designing and building models of ethorobots-including modeling the inter-species bond between domesticated animals and humans. Evidence shows that people assign emotional feelings and personality characteristics to animal species leading to cooperation and communication-crucial for designing social robots such as companion robots. Because dogs have excellent social skills with humans, current research applies humandog relationships as a template to understand HRA. Our goal of this article is twofold. First, we overview the research on how human-dog interactions are implemented as prototypes of non-human social companions in HRA. Second, we review research about attitudes that humans have for interacting with robotic dogs based on their appearance and behavior, the implications for forming attachments, and human-animal interactions in the rising sphere of robot-assisted therapy. The rationale for this review is to provide a new perspective to facilitate future research among biologists, psychologists, and engineers-contributing to the creation of innovative research practices for studying social behaviors and its implications for society addressing HRA.