Network tomography aims at inferring internal network characteristics based on measurements at the edge of the network. In loss tomography, in particular, the characteristic of interest is the loss rate of individual links. There is a significant body of work dedicated to this problem using multicast and/or unicast end-to-end probes. Independently, recent advances in network coding have shown that there are several advantages from allowing intermediate nodes to process and combine, in addition to just forward, packets. In this paper, we pose the problem of loss tomography in networks that have network coding capabilities. We design a framework for estimating link loss rates, which leverages network coding capabilities and we show that it improves several aspects of tomography, including the identifiability of links, the tradeoff between estimation accuracy and bandwidth efficiency, and the complexity of probe path selection. We discuss the cases of inferring the loss rates of links in a tree topology or in a general topology. In the latter case, the benefits of our approach are even more pronounced compared to standard techniques but we also face novel challenges, such as dealing with cycles and multiple paths between sources and receivers. This work was the first to make the connection between active network tomography and network coding, and thus opened a new research direction.