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With the rapid development of deep learning, the size of data sets and deep neural networks (DNNs) models are also booming. As a result, the intolerable long time for models' training or inference with conventional strategies can not meet the satisfaction of modern tasks gradually. Moreover, devices stay idle in the scenario of edge computing (EC), which presents a waste of resources since they can share the pressure of the busy devices but they do not. To address the problem, the strategy leveraging distributed processing has been applied to load computation tasks from a single processor to a group of devices, which results in the acceleration of training or inference of DNN models and promotes the high utilization of devices in edge computing. Compared with existing papers, this paper presents an enlightening and novel review of applying distributed processing with data and model parallelism to improve deep learning tasks in edge computing. Considering the practicalities, commonly used lightweight models in a distributed system are introduced as well. As the key technique, the parallel strategy will be described in detail. Then some typical applications of distributed processing will be analyzed. Finally, the challenges of distributed processing with edge computing will be described.