Network design and network synthesis have been the classical optimization problems in telecommunication for a long time. In the recent past, there have been many technological developments such as digitization of information, optical networks, internet, and wireless networks. These developments have led to a series of new optimization problems. This manuscript gives an overview of the developments in solving both classical and modern telecom optimization problems. The classical (still actual) network design and synthesis problems are described with an emphasis on the latest developments on modelling and solving them. Mathematical theorems will be related to the models described. This includes menger's disjoint paths theorem, the ford–fulkerson max-flow-min-cut theorem, and also gomory–hu trees and the okamura-seymour cut-condition finally, we describe recent optimization problems such as routing, wavelength assignment, and grooming in optical networks.