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This paper presents recent advances in low-latency, single-channel, deep neural network-based speech enhancement systems. The sources of latency and their acceptable values in different applications are described. This is followed by an analysis of the constraints imposed on neural network architectures. Specifically, the causal units used in deep neural networks are presented and discussed in the context of their properties, such as the number of parameters, the receptive field, and computational complexity. This is followed by a discussion of techniques used to reduce the computational complexity and memory requirements of the neural networks used in this task. Finally, the techniques used by the winners of the latest speech enhancement challenges (DNS, Clarity) are shown and compared.