BGP is the de-facto Internet routing protocol for exchanging prefix reachability information between Autonomous Systems (AS). It is a dynamic, distributed, path-vector protocol that enables rich expressions of network policies (typically treated as secrets). In this regime, where complexity is interwoven with information hiding, answering questions such as "what is the expected catchment of the anycast sites of a content provider on the AS-level, if new sites are deployed?", or "how will load-balancing behave if an ISP changes its routing policy for a prefix?", is a hard challenge. In this work, we present a formal model and methodology that takes into account policy-based routing and topological properties of the Internet graph, to predict the routing behavior of networks. We design algorithms that provide new capabilities for informative route inference (e.g., isolating the effect of randomness that is present in prior simulation-based approaches). We analyze the properties of these inference algorithms, and evaluate them using publicly available routing datasets and real-world experiments. The proposed framework can be useful in a number of applications: measurements, traffic engineering, network planning, Internet routing models, etc. As a use case, we study the problem of selecting a set of measurement vantage points to maximize route inference. Our methodology is general and can capture standard valley-free routing, as well as more complex topological and routing setups appearing in practice.Example A: A regional ISP R, whose network spans a region of two major cities, cit A and cit B , has a single upstream tier-1 ISP T A and connects to it at cit A . To avoid overloading its infrastructure in cit A , R decides to connect to another tier-1 ISP T B at cit B . However, after connecting with T B , R observes that 90% of the incoming Internet traffic still enters its network at cit A , therefore the new setup fails to balance R's load among its infrastructure in the two cities. In fact, how to select a transit provider, is a question that lacks a clear answer, and engages operators in active discussions [35]. Example B: A content provider C applies IP anycast (i.e., announces the same IP prefix) [9,13,29,33,49] from three sites. Due to traffic increase, C decides to add one more anycast site. It needs to select where to deploy and how to connect the new site, in order to best split the traffic among its sites. The ongoing research in IP anycasting, e.g., [13,28,49], indicates that this is a problem that is not well-understood yet.While a network can partially determine how other networks route traffic to it through passive (e.g., BGP data [37]) or active (e.g., traceroute, ping) measurements [2,9,13,27,32,49], measurements can provide information only for an existing deployment. However, in many applications (traffic engineering, peering decisions, network resilience, etc.) [30], it is important to know, i.e., predict, how the routing behavior of other networks will change in advance, before a network actually...