Cell images, which have been widely used in biomedical research and drug discovery, contain a great deal of valuable information that encodes how cells respond to external stimuli and intentional perturbations. Meanwhile, to discover rarer phenotypes, cell imaging is frequently performed in a high-content manner. Consequently, the manual interpretation of cell images becomes extremely inefficient. Fortunately, with the advancement of deep-learning technologies, an increasing number of deep learning-based algorithms have been developed to automate and streamline this process. In this study, we present an in-depth survey of the three most critical tasks in cell image analysis: segmentation, tracking, and classification. Despite the impressive score, the challenge still remains: most of the algorithms only verify the performance in their customized settings, causing a performance gap between academic research and practical application. Thus, we also review more advanced machine learning technologies, aiming to make deep learning-based methods more useful and eventually promote the application of deep-learning algorithms.