Micro-expressions (MEs) are involuntary facial movements revealing people's hidden feelings in high-stake situations and have practical importance in medical treatment, national security, interrogations and many human-computer interaction systems. Early methods for MER mainly based on traditional appearance and geometry features. Recently, with the success of deep learning (DL) in various fields, neural networks have received increasing interests in MER. Different from macro-expressions, MEs are spontaneous, subtle, and rapid facial movements, leading to difficult data collection, thus have small-scale datasets. DL based MER becomes challenging due to above ME characters. To date, various DL approaches have been proposed to solve the ME issues and improve MER performance. In this survey, we provide a comprehensive review of deep micro-expression recognition (MER), including datasets, deep MER pipeline, and the bench-marking of most influential methods. This survey defines a new taxonomy for the field, encompassing all aspects of MER based on DL. For each aspect, the basic approaches and advanced developments are summarized and discussed. In addition, we conclude the remaining challenges and and potential directions for the design of robust deep MER systems. To the best of our knowledge, this is the first survey of deep MER methods, and this survey can serve as a reference point for future MER research.