Recently, Deep Neural Networks (DNNs) have been shown to outperform traditional methods in many disciplines such as computer vision, speech recognition and natural language processing. A prerequisite for the successful application of DNNs is the big number of data. Even though various facial datasets exist for the case of 2D images, there is a remarkable absence of datasets when we have to deal with 3D faces. The available facial datasets are limited either in terms of expressions or in the number of subjects. This lack of large datasets hinders the exploitation of the great advances that DNNs can provide. In this paper, we overcome these limitations by introducing MimicMe, a novel large-scale database of dynamic high-resolution 3D faces. MimicMe contains recordings of 4, 700 subjects with a great diversity on age, gender and ethnicity. The recordings are in the form of 4D videos of subjects displaying a multitude of facial behaviours, resulting to over 280, 000 3D meshes in total. We have also manually annotated a big portion of these meshes with 3D facial landmarks and they have been categorized in the corresponding expressions. We have also built very powerful blendshapes for parameterising facial behaviour. MimicMe will be made publicly available upon publication and we envision that it will be extremely valuable to researchers working in many problems of face modelling and analysis, including 3D/4D face and facial expression recognition. We conduct several experiments and demonstrate the usefulness of the database for various applications. (https://github.com/apapaion/mimicme)