AI systems are increasingly being adopted across various domains and application areas. With this surge, there is a growing research focus and societal concern for actively involving humans in developing, operating, and adopting these systems. Despite this concern, most existing literature on AI and Human-Computer Interaction (HCI) primarily focuses on explaining how AI systems operate and, at times, allowing users to contest AI decisions. Existing studies often overlook more impactful forms of user interaction with AI systems, such as giving users agency beyond contestability and enabling them to adapt and even co-design the AI's internal mechanics. In this survey, we aim to bridge this gap by reviewing the state-of-the-art in Human-Centered AI literature, the domain where AI and HCI studies converge, extending past Explainable and Contestable AI, delving into the Interactive AI and beyond. Our analysis contributes to shaping the trajectory of future Interactive AI design and advocates for a more user-centric approach that provides users with greater agency, fostering not only their understanding of AI's workings but also their active engagement in its development and evolution.