Human age, as an important personal trait, can be directly inferred by distinct patterns emerging from the facial appearance. Derived from rapid advances in computer graphics and machine vision, computer-based age synthesis and estimation via faces have become particularly prevalent topics recently because of their explosively emerging real-world applications, such as forensic art, electronic customer relationship management, security control and surveillance monitoring, biometrics, entertainment, and cosmetology. Age synthesis is defined to rerender a face image aesthetically with natural aging and rejuvenating effects on the individual face. Age estimation is defined to label a face image automatically with the exact age (year) or the age group (year range) of the individual face. Because of their particularity and complexity, both problems are attractive yet challenging to computer-based application system designers. Large efforts from both academia and industry have been devoted in the last a few decades. In this paper, we survey the complete state-of-the-art techniques in the face image-based age synthesis and estimation topics. Existing models, popular algorithms, system performances, technical difficulties, popular face aging databases, evaluation protocols, and promising future directions are also provided with systematic discussions.