This paper provides a comprehensive survey of motion planning and control techniques for self-driving vehicles, particularly in urban settings. It highlights the importance of these technologies in enhancing safety, accessibility, efficiency, and convenience in automotive transportation. The paper reviews various planning and control algorithms, focusing on their effectiveness and differences in vehicle mobility models, environmental assumptions, and computational requirements. Key topics include route planning, behavioral decision-making, motion planning, and vehicle control. The survey aims to assist in system-level design choices by comparing the strengths and limitations of different approaches. The paper also discusses the challenges and advancements in motion planning, such as path planning and trajectory stabilization, and the role of feedback control in ensuring robust execution of planned motions.This paper provides a comprehensive survey of motion planning and control techniques for self-driving vehicles, particularly in urban settings. It highlights the importance of these technologies in enhancing safety, accessibility, efficiency, and convenience in automotive transportation. The paper reviews various planning and control algorithms, focusing on their effectiveness and differences in vehicle mobility models, environmental assumptions, and computational requirements. Key topics include route planning, behavioral decision-making, motion planning, and vehicle control. The survey aims to assist in system-level design choices by comparing the strengths and limitations of different approaches. The paper also discusses the challenges and advancements in motion planning, such as path planning and trajectory stabilization, and the role of feedback control in ensuring robust execution of planned motions.