Abstract: Data collection is one of the hot topics in wireless sensor networks. In traditional wireless sensor networks, those sensor nodes near the sink will deplete their energy prematurely for forwarding data sensed by both themselves and other nodes, which becomes the energy bottleneck and shortens the lifetime of whole networks. To save the energy of sensors in the wireless sensor networks, mobility elements are introduced to collect data in a lot of research work since their energy can be replenished because of mobility. However, the velocity of the mobile elements is slow, which may lead to long data collection delay. To address this problem, the problem of how to maximize the network lifetime while guaranteeing the data collection delay being less than a certain value has become a hot topic. In this paper, we investigate this kind of delay-constrained data collection methods with mobile elements in detail. We first sum up the characteristics of the delay-constrained mobile data collection methods via a novel classification. These methods are compared with each other according to a serial of key parameters. Moreover, we analyze the advantages, disadvantages and the application scope of these methods, summarize the main problems to be addressed, and further point out the future outlook on the research and application directions.