Face analysis includes a variety of specific problems as face detection, person identification, gender and ethnicity recognition; in the last two decades, significant research efforts have been devoted to the challenging task of age estimation from faces, as witnessed by the high number of published papers. The explosion of the deep learning paradigm, that is determining a spectacular increasing of the performance, is in the public eye; consequently, the number of approaches based on deep learning is impressively growing and this also happened for age estimation. The exciting results obtained have been recently surveyed on almost all the specific face analysis problems; the only exception stands for age estimation, whose last survey dates back to 2010 and does not include any deep learning based approach to the problem. This paper provides an analysis of the deep methods; these are analysed from different points of view: the network architecture together with the learning procedure, the used datasets, data preprocessing and augmentation, and the exploitation of additional data coming from gender, race and face expression. The review is completed by discussing the results obtained on public datasets, so as the impact of different aspects on system performance, together with still open issues.