Abstract: This paper is a review of theoretical, experimental and numerical studies on the entry flow of viscoelastic fluids. The viscoelastic effect and the mechanism of viscoelastic fluids in the entry converging flow are discussed from the viewpoint of micro-rheology or macro-rheology, and the constitutive equations of the fluids suitable for entry flow problems are analyzed. Finally, the research progress about the entry flow of viscoelastic fluids during recent ten years are briefly reviewed.