This chapter examines human-in-the-loop (HITL) and human-on-the-loop (HOTL) frameworks in artificial intelligence (AI) systems, focusing on design principles and implementation factors that improve human controllability over AI systems. HITL architectures involve active human decision-making to enhance accuracy and accountability, while HOTL systems operate with more algorithmic autonomy under human supervision and intervention. The chapter discusses human-centered AI (HCAI) principles, core theoretical ideas, ethical issues, and operational challenges of these frameworks, evaluating user-centered design, participatory methods, and scenario-based approaches. Through empirical studies of applications in healthcare, autonomous systems, and finance, the chapter shows how HITL and HOTL implementations boost system reliability and efficiency. By critically comparing the benefits and limitations of both approaches, this chapter offers a foundational framework for developing HCAI systems that emphasize trust, transparency, human controllability, ethics, and user experience as key design principles.