The pipe exhibits complex vibration characteristics under the action of flowing fluid and external excitations. Investigations on design, optimization, and application of the control schemes for the vibration of pipes are still active since more and more new configurations are needed in more and more new practical circumstances. The present work provides a comprehensive review of state-of-the-art researches related to passive control of vibration of pipes conveying fluid. The work begins with a survey of the important vibration control and dynamics characteristics of pipes conveying fluid. Secondly, the general characteristics of the research on the dynamics of the pipe are introduced. Then, the research progress of passive control of vibration of pipes conveying fluid is summarized. At last, some further promising directions are suggested. That this paper will help researchers to understand the research status of passive control of pipe vibration, and can arouse more attentions to vibration control of pipes, so as to promote the efficient and safe operation of pipe systems.