## 1 Introduction  
Modern communication network infrastructures exhibit the tendency of more heterogeneous and larger topologies, larger volumes of transferred data, and faster transmission rates. Traditional management and monitoring frameworks require reconsideration and, in some cases, clean-slate approaches in order to cope with the emerging scales of operation. Network monitoring is one of the prominent functions that needs to be revisited under the aforementioned perspective and will be a determinant factor for creating advanced communication infrastructures in the future Internet. Towards this direction, in this review, we focus specifically on network tomography. _Network tomography_ (NT) is a network-monitoring technique that involves estimating network performance and Quality of Service (QoS) parameters based on traffic measurements at a limited subset of the network's nodes (where each node may represent an end-system, a router, or a subnetwork) [1, 2]. The goal is to infer desired characteristics, which are not easily measured directly, by their aggregate values. These values are possible to obtain through measurements collected at accessible nodes/links under the administrative responsibility of the network authority. Among other benefits, such an approach mitigates the need for special purpose cooperation and participation from the various network elements while reducing the associated traffic-overhead footprint to the network load compared to well-known tools such as traceroute and ping, which require Internet Control Message Protocol (ICMP) responses from routers. Furthermore, this approach avoids the current problem of an increasing number of Internet routers blocking traceroute requests due to privacy and security concerns (such routers are referred to as anonymous routers). Network tomography can be realized in many different ways, each focusing on different goals. Three main categories can be identified: (1) _link-level parameter estimation_, (2) _path-level traffic intensity estimation_, and (3) _topology inference_, which are elaborated on in Section 2.2. These goals can be achieved by means of various approaches such as hierarchical clustering, Expectation-Maximization (EM) algorithm, Markov Chain Monte Carlo (MCMC) sampling, Method of Moments (MoM) estimation, and other classical and Bayesian statistical methods. In this review, we focus on two families of approaches, namely network coding and compressed sensing, due to the fact that (a) they were recently introduced in the field of NT, (b) they exhibit great potential for designing highly accurate schemes with low complexity, and( c) they form two independent methods, which can be used in a broader spectrum of problems and in a complementary fashion. _Network coding_ (NC) has received considerable attention in recent years due to its potential of maximizing network resource utilization up to the theoretical upper bound (i.e., max-flow/min-cut) and its promising applications in the context of ad hoc networks, overlay infrastructures, and sensor networks. The basic concept of network coding is that the intermediate nodes of the network (i.e., not sources and destinations) are able to linearly combine, i.e., perform additions and multiplications of the packets they receive, and to send out the resulted linear combinations on their outgoing links [3; 4]. The packets received eventually at the destination(s) can be written as a linear combination of the packets sent out by the source(s). This broadcasting nature of network coding ensures that a transmitted probe will traverse almost every path between the two boundary nodes (located at the network edge) and can be exploited in the context of network tomography. In particular, the observations obtained at the end-hosts depend on the underlying network topology and can be used to deterministically recover it.