Facial beauty has engaged researchers in psychology, evolution, plastic surgery, and computer science for many centuries. This chapter illustrates the significance of facial beauty research and traces how studies about attractive faces moved from qualitative rules to data-driven analysis. We review findings on universal and culture-modulated preference of beauty, and we introduce the emergence of computational aesthetics in two-dimensional imagery. We present recent progress in 2D facial aesthetics analysis, with a focus on approaches developed through machine learning and deep learning techniques. We then outline the limits of 2D pipelines under pose, illumination, and expression shifts and the need for richer shape information, which motivates a trend to three-dimensional analysis. We introduce the field of 3D facial aesthetics analysis and present a concise overview of its fundamental concepts. We also point out some concerns regarding the current state of aesthetic research, such as interpretability, imbalance, and unfairness. Lastly, we provide an outline of this book.