The overhead of internal network monitoring motivates techniques of network tomography. Network coding (NC) presents a new opportunity for network tomography as NC introduces topology-dependent correlation that can be further exploited in topology estimation. Compared with traditional methods, network tomography with NC has many advantages such as the improvement of tomography accuracy and the reduction of complexity in choosing monitoring paths. In this paper we first introduce the problem of tomography with NC and then propose the taxonomy criteria to classify various methods. We also present existing solutions and future trend. We expect that our comprehensive review on network tomography with NC can serve as a good reference for researchers and practitioners working in the area.