Age progression and regression is a task that aims at rendering face images with or without the "aging" effects. The problem is originally generated from the psychophysics and human perception community but now has found tremendous interests in the computer vision community in recent years. In this paper, we give a detailed analysis of the facial aging problem and conduct a comprehensive survey on the existing methods. There are many different methods available for face aging rendering, and each has its own advantages and purpose. We categorize the existing methods into three classes: physical-based models, example-based methods, and Deep learning-based methods. The first two classes are more traditional methods that have been developed in the last few decades, while the deep learning-based methods are leveraged on the huge success of the deep learning models that emerged in recent years. We review the representative works in each category and offer insights into future research on this topic.