Robots are widely used in many tedious and simple works. But, with the advance of technology, they are expected to work in more complex environments and participate in more challenging tasks. Correspondingly, more intelligent and robust algorithms are required. As a domain having been explored for decades, task and motion planning (TAMP) methods have been applied in various applications and have achieved important results, while still being developed, particularly through the integration of more machine learning approaches. This paper summarizes the development of TAMP, presenting its background, popular methods, application environment, and limitations. In particularly, it compares different simulation environments and points out their advantages and disadvantages. Besides, the existing methods are categorized by their contribution and applications, intending to draw a clear picture for beginners.