Time-lapse microscopy images generated by biological experiments have been widely used for observing target activities, such as the motion trajectories and survival states. Based on these observations, biologists can conclude experimental results or present new hypotheses for several biological applications, i.e. virus research or drug design. Many methods or tools have been proposed in the past to observe cell and particle activities, which are defined as single cell tracking and single particle tracking problems, by using algorithms and deep learning technologies. In this article, a review for these works is presented in order to summarize the past methods and research topics at first, then points out the problems raised by these works, and finally proposes future research directions. The contributions of this article will help researchers to understand past development trends and further propose innovative technologies.