Network security metrics (NSMs) based on models allow to quantitatively evaluate the overall resilience of net- worked systems against attacks. For that reason, such metrics are of great importance to the security-related decision-making process of organizations. Considering that over the past two decades several model-based quantitative NSMs have been pro- posed, this article presents a deep survey of the state-of-the- art of these proposals. First, to distinguish the security metrics described in this survey from other types of security metrics, an overview of security metrics, in general, and their classifications is presented. Then, a detailed review of the main existing model- based quantitative NSMs is provided, along with their advantages and disadvantages. Finally, this survey is concluded with an in-depth discussion on relevant characteristics of the surveyed proposals and open research issues of the topic.