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Face recognition is one of the most popular and long-standing topics in computer vision. With the recent development of deep learning techniques and large-scale datasets, deep face recognition has made remarkable progress and been widely used in many real-world applications. Given a natural image or video frame as input, an end-to-end deep face recognition system outputs the face feature for recognition. To achieve this, a typical end-to-end system is built with three key elements: face detection, face alignment, and face representation. The face detection locates faces in the image or frame. Then, the face alignment is proceeded to calibrate the faces to the canonical view and crop them with a normalized pixel size. Finally, in the stage of face representation, the discriminative features are extracted from the aligned face for recognition. Nowadays, all of the three elements are fulfilled by the technique of deep convolutional neural network. In this survey article, we present a comprehensive review about the recent advance of each element. To start with, we present an overview of the end-to-end deep face recognition. Then, we review the advance of each element, respectively, covering many aspects such as the to-date algorithm designs, evaluation metrics, datasets, performance comparison, existing challenges, and promising directions for future research. Also, we provide a detailed discussion about the effect of each element on its subsequent elements and the holistic system. Through this survey, we wish to bring contributions in two aspects: first, readers can conveniently identify the methods which are quite strong-baseline style in the subcategory for further exploration; second, one can also employ suitable methods for establishing a state-of-the-art end-to-end face recognition system from scratch.