The development of pipeline systems and the creation of new schemes, with the inclusion of additional equipment, poses high demands on the safety and reliability of the operation of injection plants, pumping stations, as well as on the elements of pipelines responsible for timely protection of the system in the event of emergency situations. The practice of operating long and short pipelines shows that fluctuations in pressure and flow caused by the operation of injection plants, as well as overloads of impact type, caused, in particular, by the operation of shut-off elements, result in additional dynamic loads on the pipeline, which can lead to accidents and catastrophes with severe consequences, human casualties. During the transient process in the individual sections of the pipeline, especially at the inlet and outlet of the injection plant, the pressure change can be so abrupt that it is possible to destroy the walls of the pipeline. Therefore, the problem of creating effective means of damping wave processes and hydraulic shocks has not lost its relevance for many decades. The article briefly describes the history of development of calculation methods of unsteady movement of a viscous and compressible fluid. The main problems are denoted in the practical operation of hydraulic systems, including various types of equipment. The references to articles which provide analysis of various aspects related to this subject are given.