Thyroid nodule is one of the most common clinical nodular lesions in adults, and its incidence rate is always high. Thyroid nodule can be classified into benign and malignant, and the latter is thyroid cancer, which can cause difficulties in breathing and swallowing, and even endanger the life of patients. Therefore, the identification of benign and malignant thyroid nodule is the primary problem in the diagnosis and treatment of thyroid nodule. Deep learning can automatically extract nodule features and complete the preliminary classification of benign and malignant thyroid nodule. With the continuous improvement of classification accuracy of deep learning, it has become an important means of auxiliary diagnosis of benign and malignant thyroid nodule. To better study the classification and auxiliary diagnosis of benign and malignant thyroid nodule, we introduce the commonly used indicators for the evaluation of nodule classification performance, and classify them according to the convolutional neural network, Transformer, deep neural network, generative adversarial network, transfer learning, ensemble learning, and computer-aided diagnosis system based on deep learning, and elaborate their application in the classification of benign and malignant thyroid nodule. We conduct a comprehensive comparative analysis, summarize the existing problems in the current research, and provide prospects for future research directions.