To ensure the secure operation of space assets, it is crucial to employ ground and/or space-based surveillance sensors to observe a diverse array of anthropogenic space objects (ASOs). This enables the monitoring of abnormal behavior and facilitates the timely identification of potential risks, thereby enabling the provision of continuous and effective Space Situational Awareness (SSA) services. One of the primary challenges in this endeavor lies in optimizing the tasking of surveillance sensors to maximize SSA capabilities. However, the complexity of the space environment, the vast number of ASOs, and the limitations imposed by available sensor resources present significant obstacles to effective sensor management. To tackle these challenges, various sensor tasking methods have been developed over the past few decades. In this paper, we comprehensively outline the fundamental characteristics of sensor tasking missions, and later examine the corresponding objective functions and algorithms employed for efficient optimization, respectively. Furthermore, we explore the practical application of sensor tasking methods in diverse organizations and provide insights into potential directions for future research, aiming to stimulate further advancements in this field.