Classification of HEp-2 cell patterns plays a significant role in the indirect immunofluorescence test for identifying autoimmune diseases in the human body. Many automatic HEp-2 cell classification methods have been proposed in recent years, amongst which deep learning based methods have shown impressive performance. This paper provides a comprehensive review of the existing deep learning based HEp-2 cell image classification methods. These methods perform HEp-2 image classification in two levels, namely, cell-level and specimen-level. Both levels are covered in this review. In each level, the methods are organized with a deep network usage based taxonomy. The core idea, notable achievements, and key advantages and weakness of each method are critically analyzed. Furthermore, a concise review of the existing HEp-2 datasets that are commonly used in the literature is given. The paper ends with an overview of the current state-of-the-arts and a discussion on novel opportunities and future research directions in this field. It is hoped that this paper would give readers a comprehensive reference of this novel, challenging, and thriving field.