•This paper was written by scanning the literature extensively.•Face age synthesis is the determination of how a person looks in the future or in the past by reconstructing their facial image.•Determining the change in the human face over the years is a critical process for cross-age face recognition systems in forensic issues such as finding missing people and fugitive criminals.•With the implementation of deep learning methods, better quality and photo-realistic images began to be produced.•We group the studies in the literature under two categories: classical methods and deep learning methods.•We review both categories in the methods used, evaluation methods, and databases. Face age synthesis is the determination of how a person looks in the future or the past by reconstructing their facial image. Determining the change in the human face over the years is a critical process for cross-age face recognition systems in forensic issues such as finding missing people and fugitive criminals. Therefore, it is a subject that has attracted attention in recent years. With the implementation of deep learning methods, better quality and photo-realistic images began to be produced. However, researchers continue to improve both aging accuracy and identity preservation requirements. We group the studies in the literature under two categories: classical methods and deep learning methods. We review both categories in the methods used, evaluation methods, and databases.