Robust Design is an important method for improving product quality, manufacturability, and reliability at low cost. Taguchi's introduction of this method in 1980 to several major American industries resulted in significant quality improvement in product and manufacturing process design. While the robust design objective of making product performance insensitive to hard-to-control noise was recognized to be very important, many of the statistical methods proposed by Taguchi, such as the use of signal-to-noise ratios, orthogonal arrays, linear graphs, and accumulation analysis, have room for improvement. To popularize the use of robust design among engineers, it is essential to develop more effective, statistically efficient, and user-friendly techniques and tools. This paper first summarizes the statistical methods for planning and analyzing robust design experiments originally proposed by Taguchi; then reviews newly developed statistical methods and identifies areas and problems where more research is needed. For planning experiments, we review a new experiment format, the combined array format, which can reduce the experiment size and allow greater flexibility for estimating effects which may be more important for physical reasons. We also discuss design strategies, alternative graphical tools and tables, and computer algorithms to help engineers plan more efficient experiments. For analyzing experiments, we review a new modeling approach, the response model approach, which yields additional information about how control factor settings dampen the effects of individual noise factors; this helps engineers better understand the physical mechanism of the product or process. We also discuss alternative variability measures for Taguchi's signal-to-noise ratios and develop methods for empirically determining the appropriate measure to use.