As the global population ages, there is an increase in demand for assistive technologies that can alleviate the stresses on healthcare systems. The growing field of socially assistive robotics (SARs) offers unique solutions that are interactive, engaging, and adaptable to different users’ needs. Crucial to having positive human-robot interaction (HRI) experiences in senior care settings is the overall design of the robot, considering the unique challenges and opportunities that come with novice users. This paper presents a novel study that explores the effect of SAR design on HRI in senior care through a results-oriented analysis of the literature. We provide key design recommendations to ensure inclusion for a diverse set of users. Open challenges of considering user preferences during design, creating adaptive behaviors, and developing intelligent autonomy are discussed in detail. SAR features of appearance and interaction mode along with SAR frameworks for perception and intelligence are explored to evaluate individual developments using metrics such as trust, acceptance, and intent to use. Drawing from a diverse set of features, SAR frameworks, and HRI studies, the discussion highlights robot characteristics of greatest influence in promoting wellbeing and aging-in-place of older adults and generates design recommendations that are important for future development.