With the rapid growth in foreign trade business and the continuous expansion of customs functions, the amount of data obtained by customs monitoring systems has drastically increased, and risk management techniques have been widely used in the customs field. Risk assessment, as an important part of risk management, can help departments of customs to understand the possibility and impact of risks in advance. Assessing the risks of import and export enterprises is an important task for customs. However, the assessment is challenging because of the large-scale of data, rapidly changing information, and inherent fuzziness. To address this issue, this survey summarizes the existing risk assessment methods, combines the preliminaries of fuzzy logic and neural networks, and applies the representative risk assessment models in the risk assessment of import and export enterprises. The risk assessment models based on fuzzy logic and neural networks can handle vague and uncertain data and improve the efficiency of risk assessment through adaptive and learning capabilities. The combination of theoretical and simple case suggests that the risk assessment method based on fuzzy logic and neural networks has good feasibility for import and export enterprises, and provides valuable references for developing effective risk assessment models of import and export enterprises in the future.