This paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). Modern autonomous systems, such as flying, legged, and wheeled robots, are characterized by high-dimensional nonlinear dynamics, which pose challenges for model-based safety-critical control design. The paper introduces a unified formulation of techniques that construct CBFs for complex systems from CBFs for simpler systems. These ideas are illustrated through formal results, numerical examples, and case studies of real-world systems. The paper discusses the theoretical foundations of CBFs, their application across different domains, and the challenges in constructing CBFs for high-dimensional systems. It also explores the use of reduced-order models (ROMs) to construct CBFs for complex systems, demonstrating their effectiveness in controlling seemingly complex systems in a computationally efficient manner. The paper highlights the importance of safety in autonomous systems and the role of CBFs in ensuring safety. It also addresses the challenges of constructing CBFs for systems with uncertainty and presents various approaches to overcome these challenges. The paper concludes with a discussion of the limitations of the paradigms presented and open research directions.This paper presents a tutorial on constructive safety-critical control via reduced-order models and control barrier functions (CBFs). Modern autonomous systems, such as flying, legged, and wheeled robots, are characterized by high-dimensional nonlinear dynamics, which pose challenges for model-based safety-critical control design. The paper introduces a unified formulation of techniques that construct CBFs for complex systems from CBFs for simpler systems. These ideas are illustrated through formal results, numerical examples, and case studies of real-world systems. The paper discusses the theoretical foundations of CBFs, their application across different domains, and the challenges in constructing CBFs for high-dimensional systems. It also explores the use of reduced-order models (ROMs) to construct CBFs for complex systems, demonstrating their effectiveness in controlling seemingly complex systems in a computationally efficient manner. The paper highlights the importance of safety in autonomous systems and the role of CBFs in ensuring safety. It also addresses the challenges of constructing CBFs for systems with uncertainty and presents various approaches to overcome these challenges. The paper concludes with a discussion of the limitations of the paradigms presented and open research directions.