As robotic products become more integrated into daily life, there is a greater need to understand authentic and real-world human-robot interactions to inform product design. Across many domestic, educational, and public settings, robots interact with not only individuals and groups of users, but also families, including children, parents, relatives, and even pets. However, products developed to date and research in human-robot and child-robot interactions have focused on the interaction with their primary users, neglecting the complex and multifaceted interactions between family members and with the robot. There is a significant gap in knowledge, methods, and theories for how to design robots to support these interactions. To inform the design of robots that can support and enhance family life, this paper provides (1) a narrative review exemplifying the research gap and opportunities for family-robot interactions and (2) an actionable family-centered framework for research and practices in human-robot and child-robot interaction.