Currently, technological possibilities for implementing multi-service networks include both single technology ATM or IP networks and multi-technology networks such as SONET-based or flat networks. However, regardless of the technology employed, the synthesis problem - to optimally route traffic and divide the network's transmission resources between it's virtual links - remains of prime importance. In this paper, we review, compare, and classify the extensive recent literature concerning multi-service network synthesis methods. In order to do this, we propose a typology based on switching and control strategies and a general notation that reflects the layered nature of the network. Technology independent mathematical models describe the various, essentially different, approaches presently found in the literature.