Face Age Progression (FAP) refers to synthesizing face images while simulating ageing effects, thus enabling predicting the future appearance of an individual. The generation of age-progressed face images brings benefits for various applications, ranging from face recognition systems to forensic investigations and digital entertainment. In particular, the recent success achieved with deep generative networks significantly leveraged the quality of age-synthesized face images in terms of visual fidelity, ageing accuracy and identity preservation. However, the high number of contributions in recent years requires systematically structuring new findings and ideas to identify a common taxonomy, accelerate future research and reduce redundancy. Therefore, we present a comparative analysis of recent deep learning based face age progression methods for both adult and child-based face ageing, broken down into three high-level concepts: translation-based, condition-based, and sequence-based FAP. Further, we offer a comprehensive summary of the most common performance evaluation techniques, cross-age datasets, and open challenges to steer future research in the right direction.