Network monitoring systems are deployed by Internet Service Providers (ISP) and enterprises to obtain network performance information and enhance the global network performance. A constant monitoring is also required to enforce and ensure both connectivity and security of the infrastructure. Designing and developing the infrastructure and optimization algorithms for network monitoring system have raised a great deal of interest recently. One of the key issues in this domain is to minimize the overhead in terms of deploying cost, maintenance cost and additional traffic. Due to different measurement approaches and polling infrastructure, there are many network measurement deploying models. Unfortunately, the optimization problems of these models are generally NP-hard. These optimization problems used to be solved by integer programming, designing approximation algorithms or mapping it to classic optimization problems. In this paper, the chief researches of network measurement deploying models and optimization algorithms in the world are introduced. Lastly, some open issues are presented to be further studied in the network measurement deploying models field.