With the rapid development of the Internet of Things (IoT) and communication technology, Deep Neural Network (DNN) applications have been widely used in IoT devices. However, due to resource constraints on these devices, IoT devices cannot support complicated DNN operation effectively and thus fail to fulfill the requirements of Quality of Service (QoS) of mobile users. One promising approach is to migrate the DNN model to a remote cloud server to reduce the computing burden on IoT devices. Unfortunately, it still suffers from high delay and low bandwidth when communicating with cloud servers. Although the transmission delay of the edge server is low, its computing capacity lacks scalability and elasticity. In this paper, we describe a DNN model migration framework to overcome the above challenges, which consists of three parts: DNN model preprocessing, partition-offloading plan, and partition-uploading plan. Accordingly, we introduce the operation of the DNN migration and the available methods for each part. In addition, we improve the DNN partition-uploading plan in a multi-user edge-cloud collaborative computing environment. Finally, we highlight the important challenges of achieving more efficient DNN migration and point out the unresolved issues of DNN migration, which may shed light on future research directions.