Automotive industry today is challenged by numerous complex and often conflicting constraints and requirements such as compress vehicle design cycle time, lower the weight and cost of vehicles, and improve product performances, e.g., durability, NVH, safety, quality, reliability, etc. To satisfy these stringent requirements, automobile manufacturers are increasingly relying on Computer-Aided Engineering (CAE) and the use of more formal and structured approaches for product development. Numerical optimization is a systematic tool for considering all disciplines and finds a compromise solution. In addition, as most CAE simulations are computation intensive, special optimization methods and processes are often required. This presentation will focus on historical developments and applications of numerical optimization and robustness methods for vehicle designs. It will address significant technologies, such as Topology Optimization, Multi-disciplinary Design Optimization, Robust, Reliability-Based Design Optimization, and Process Integration and Design Optimization.