Microfluidics, which can precisely manipulate micron-sized particles, has been widely used in medical, pharmaceutical, biological and chemical fields. The passive manipulation technologies without external field effect have become a research hotspot because of their simplicity and autonomy. Compared with other passive manipulation technologies, viscoelastic focusing technology makes it easier to achieve three-dimensional focusing of particles, and can manipulate particles with a large-scale span and a wide range of fluid flow. Therefore, this paper reviews the latest research on viscoelastic fluids in particle passive manipulation applications. Firstly, the force mechanism of particles in viscoelastic fluid in different microchannel structure is introduced. Then, the research progress of viscoelastic focusing, sorting, mixing and other viscoelastic particle manipulation applications is further elaborated. Finally, the numerical simulation method for studying the flow characteristics of viscoelastic fluids and the movement law of particles in it are introduced, and some prospects for the future development of viscoelastic microfluidics are made based on the analysis of existing problems.