The free access to large-scale public databases, together with the fast progress of deep learning techniques, in particular Generative Adversarial Networks, have led to the generation of very realistic fake content with its corresponding implications towards society in this era of fake news. This survey provides a thorough review of techniques for manipulating face images including DeepFake methods, and methods to detect such manipulations. In particular, four types of facial manipulation are reviewed: i) entire face synthesis, ii) identity swap (DeepFakes), iii) attribute manipulation, and iv) expression swap. For each manipulation group, we provide details regarding manipulation techniques, existing public databases, and key benchmarks for technology evaluation of fake detection methods, including a summary of results from those evaluations. Among all the aspects discussed in the survey, we pay special attention to the latest generation of DeepFakes, highlighting its improvements and challenges for fake detection. In addition to the survey information, we also discuss open issues and future trends that should be considered to advance in the field.