Nowadays, vulnerability attacks occur frequently. Due to the information asymmetry between attackers and defenders, vulnerabilities can be divided into known and unknown. Existing researches mainly focus on the risk assessment of known vulnerabilities. However, unknown vulnerabilities are more threatening and harder to detect. Therefore, unknown vulnerability risk assessment deserves the widespread attention. To model the exploit process, directed graph models are applied to vulnerability risk assessment. And security metrics are used to quantify the exploitability of vulnerabilities. In this paper, according to the data source of nodes, related works of unknown vulnerability risk assessment based on directed graph models are divided into two types. One is based on network-level data, the other is based on system-level data. The former is to visualize the network status, while the latter is to reflect the running process of the system. The concept and purpose of these directed graph models are given at first. Then, these models are analyzed from three aspects, including advantages, flaws and solutions. After that, challenges and solutions of unknown vulnerability risk assessment based on directed graph models are given. Meantime, security metrics for unknown vulnerability risk assessment based on directed graph models are summarized and classified. Finally, future work directions of unknown vulnerability risk assessment are discussed from the perspective of techniques and application trends. Consequently, this paper can fill in the lack of current survey on unknown vulnerability risk assessment based on directed graph models. INDEX TERMS Directed graph model, risk assessment, security metric, unknown vulnerability.