Abstract: In this paper, various physical and mathematical models ofpipes conveying fluid are summarized. Under some assumptions for the fluidin the pipe, the mathematical models of the beam-pipe are proposed togovern the dynamics of straight or curve pipes with internal radii lessthan their length. The proposed models arediscussed in details. The governing equations of shell-pipe are given forshort and thin pipes subjected to dynamic pressure in the pipes. Then,therecent research development is reviewed on nonlinear vibration,stability, bifurcation and control for pipes conveying fluid. The futuretrends and advances are proposed. From the history ofnonlinear dynamics, one may see that it is very important to choose sometypical systems as models, such as van der Pol, Duffing, Mathieu, Lorenz andso on, for studying low dimensional systems. The motivation of this paperis to represent fluid-reduced vibrations as one of typical nonlinearproblems. It may be considered as a model to investigate nonlinear dynamicsin high dimensional systems since its engineering background is intuitiveand easy to be understood, vibrations of shell and beam are included, itsmathematical model is simple but may present rather rich dynamics, and the results of the mathematical analysis is easy to be explained andapplied. It is expected to establish models of analysis for high-dimensionalsystems and to develop nonlinear dynamics in terms of discussions in this paper.In addition, it may also provide some guidance for establishingthe control theory.