Abstract The vibrations and stability of slender structures subjected to axial flow or axially towed in quiescent fluid are discussed in this paper. A selective review of the research undertaken on it is presented. It is endeavoured to show that slender structures subjected to axial flow or axially towed in quiescent fluid are capable of displaying rich dynamical behavior. The basic dynamics of straight and curved pipes conveying fluid (with or without motion constraints), carbon nanotubes conv ...