In recent years, deep learning has been widely applied to various classification tasks due to its capability in automatically extracting features and superior classification performance. Research on the classification of lung nodules has gradually shifted from traditional methods that involve manual feature extraction to deep learning-based classification approaches. To better investigate the benign-malignant classification of lung nodules in CT images, the current status of deep learning methods based on convolutional neural network (CNN) in the research of benign and malignant classification of lung nodules is summarized. Firstly, this paper introduces commonly used publicly available datasets for lung nodule classification, including their contents, limitations, and download sources. Secondly, it outlines commonly used performance evaluation metrics. It then highlights the recent research work on deep learning methods for lung nodule classification: current methods for lung nodule classification are categorized as using only CNN, introducing an attention mechanism in CNN, multi-view learning, multi-modal learning, and using migration learning, adversarial neural networks, and other methods, repectively, from the level of network structure and data. Meanwhile, this paper further summarizes the network structures, advantages and disadvantages of these classification methods. A comparative analysis is conducted on the benign-malignant classification performance of lung nodule classification methods based on these aspects over the past three years using publicly available nodule datasets. Finally, this paper discusses current challenges and explores further research directions in the field of lung nodule classification.