Cervical cytology image analysis is indispensable for the detection of abnormal cervical cells. Traditionally, manual screening is time-consuming and labor-intensive. Therefore, a lot of deep learning (DL)-based automatic detection methods have been employed in this field to provide timely, accurate and objective results. In this study, we systematically review the current developments in cervical cell image analysis with DL methods. Specifically, we first present the most popular DL models that are widely applied in cervical cell analysis. Second, we describe the methodology for conducting this review. Third, we provide all publicly available datasets related to cervical cell images to the best of our knowledge. Then, we introduce relevant evaluation metrics and loss functions. Next, we summarize and assort the applications for cervical cell classification and segmentation. Afterwards, we discuss about current challenges and future research directions in this field. Finally, we draw the conclusion of this review.According to the analysis, we conclude that the studies based on DL models have maintained an increasing trend in recent years, which indicates the potential of DL in cervical cell image analysis. In cervical cell image classification, CNN is the most commonly used DL model. Among CNN models, we can find that VGGNet and ResNet are the most popular network architectures for the classification of cervical cells. Transformer is the second commonly used DL model. Moreover, Herlev and SIPaKMeD are the most popular public datasets used for cervical cell classification. In cervical cell segmentation, U-Net and FCN are the two most popular DL architectures. In addition, ISBI2014 and Herlev datasets are the most frequently used among the existing publicly available segmentation datasets. However, there are some issues in this field, such as poor cervical cell classification performance as a result of similar pathological properties between different cell categories. Therefore, it is necessary to develop more effective methods with DL models to improve these issues in the future research.