One of the main stages of Network on Chip (NoC) is task mapping where the application tasks are mapped to the processing resources. Task mapping decisions have a direct impact on the NoC performance and can be classified as static or dynamic mapping methods. In this paper, we carry out a comprehensive systematic study of task mapping schemes in various NoCs. For this purpose, firstly, an overview of the task mapping's main concepts is presented. Then, a taxonomy of the mapping schemes regarding their objectives and applied mapping factors is presented and the studied schemes are categorized into fault-tolerant schemes, congestion-aware schemes, communication-aware approaches, temperature-aware methods, and energy-aware schemes. Afterward, their main contributions, provided services, and drawbacks of the proposed studies in the literature are illustrated. Moreover, a comprehensive discussion of various features of the investigated mapping methods is presented and issues such as the applied algorithms, simulators, datasets, and evaluation metrics are discussed. Finally, the concluding issues and open research areas are highlighted.