Age estimation is a technique for predicting human ages from digital facial images, which analyzes a person's face image and estimates his/her age based on the year measure. Nowadays, intelligent age estimation and age synthesis have become particularly prevalent research topics in computer vision and face verification systems. Age synthesis is defined to render a facial image aesthetically with rejuvenating and natural aging effects on the person's face. Age estimation is defined to label a facial image automatically with the age group (year range) or the exact age (year) of the person's face. In this case study, we overview the existing models, popular techniques, system performances, and technical challenges related to the facial image-based age synthesis and estimation topics. The main goal of this review is to provide an easy understanding and promising future directions with systematic discussions.