A pipeline network is a collection of elements such as pipes, compressors, pumps, valves, regulators, heaters, tanks, and reservoirs interconnected in a specific way. Pipeline networks constitute major bulk carriers for crude oil, natural gas, water, and petroleum products. Networks of pipes and valves form an integral part of pressure-relieving and fire–water systems designed to handle contingencies in the operation of process units. The behavior of the network is governed by two factors: the specific characteristics of the elements and the connection of these elements. The first factor is determined by the physical laws and the second by the topology of the network. The simplest form of network synthesis involves a single input and a single output—the problem of optimal routing of a pipeline. Another form involves a tree—the synthesis of a gathering or distribution network. The chapter assesses the status of the relevant technology with particular reference to formulation of problems and methods of solution. It is concerned with the previous technical literature of the last few years. It also discusses some digital computation methods of designing pipeline networks.