Wireless sensor network (WSN) is one of the most significant technologies that gets much attention from researchers due to its promising applications in various environments. Mobility in wireless sensor networks contributes significantly to improving the performance of terrestrial wireless sensor networks (TWSNs) and underwater wireless sensor networks (UWSNs). This research's primary goal is to highlight the roles of mobility and mobile element tasks in enhancing terrestrial and underwater wireless sensor networks. Our systematic literature review (SLR) analyzed studies published between the periods of 2003 and January 2020. Out of 1762 studies retrieved by searching six online digital libraries and other resources, only 107 of them were selected for primary studies based on selection criteria and relevant to three identified research questions. This was followed by data extraction from the primary studies for answering the three SLR questions. The study reveals that mobility plays an essential role in improving network performance in TWSNs and UWSNs, especially in the aspects of coverage, energy efficiency, throughput, and connectivity. The study also identifies the tasks of the mobile elements in TWSNs and UWSNs, including data collection, localization, and charging. Moreover, it demonstrates the parameters of the mobile elements that should be considered when building networks. Finally, this study concludes by highlighting some open research issues that can be considered for future research.