Social Assistive Robotics (SAR) is an emerging form of assistive technology that encompasses all robotic systems based on artificial intelligence, employing various forms of communication in order to support and motivate users in performing their tasks. What have been extensively studied, however, are humanoid robots, not zoomorphic robots, also called petbots, which, although promising, are still a relatively unexplored category. The animal-like design, which makes them appear less threatening, and their ability to improve communication skills by promoting social interactions, make petbots potential agents to support the emotional, cognitive and social well-being of vulnerable groups, such as children with autism spectrum disorder (ASD) and elderly people with dementia or mild cognitive impairment (MCI). This review adopts a structured narrative approach to synthesise recent peer-reviewed literature on the use of petbots in therapeutic and care settings, specifically selecting papers published from 2019 to 2025. Models such as Paro, Aibo, Loona, Keepon and Probo were included based on their relevance and presence in empirical research. To contextualise their role, the review also compares studies on humanoid SAR robots and considers ethical, cultural and design factors influencing user acceptance and real-world implementation.