Evolving market trends, characterized by an increasing demand for personalized products with short life cycles and variable demands, pose a significant challenge to the industry. One of the industry's strategies is to adopt robotic assembly systems to improve productivity and increase system flexibility. The widespread adoption of robots in assembly processes is evident; however, success is not guaranteed with implementation alone. Equally critical is addressing assembly planning and scheduling problems in robotic systems. To facilitate understanding, this review offers, in Section 2, a classification of robotic assembly systems, with an emphasis on a new layout termed the robotic matrix-structure assembly system. Section 3 classifies the planning and scheduling problems applied to the robotic assembly systems. In Section 4, we discuss the approaches and techniques used to formulate and solve the planning and programming challenges. Finally, statistical data are presented to illustrate current research trends and identify gaps for future research.