The increasing material costs and the rapid advances in computing technology have both motivated and promoted the study of network problems that arise in several different application domains. This dissertation consists of four chapters on network applications in transportation, telecommunications, and supply chain management. The core of our research is to apply heuristic search procedures and combinatorial optimization techniques to various practical problems. In the second chapter we investigate the split delivery vehicle routing problem (SDVRP), where a customer's demand can be split among several vehicles. The third chapter deals with the regenerator location problem (RLP) that arises in optical networks. The fourth chapter solves the parametric uncapacitated network design problems on series-parallel graphs, which have potential application in supply chain management. In the fifth chapter we study the arc routing problem that arises in the small package delivery industry. The last chapter summarizes the dissertation. The results in this dissertation indicate that the methodologies developed to solve the network problems in the four different applications are quite efficient. Consequently, when applied in practice, they have the potential to significantly improve the operational efficiency of organizations in the relevant application domains.