This paper reviews Genichi Taguchi's contributions to the field of quality and manufacturing engineering from both a statistical and an engineering viewpoint. His major contributions are first listed and then described in a systematic and analytical manner. The concepts underlying Taguchi's univariate quality loss functions (QLFs), his orthogonal arrays (OAs), robust designs, signal-to-noise (S/N) ratios, and their corresponding applications to quality and process engineering are examined and described in great detail. Some of Taguchi's OAs are related to the classical (fractional) factorial designs (a field that was started by Sir Ronald A. Fisher in the early 1920s). The applications of Taguchi's robust (parameter and tolerance) designs to manufacturing engineering are illustrated through designed experiments.