Review devoted to the analysis of literature for 1973-1983. on the dynamics of distribution and decay of free thin jets and films of drip fluids with different rheological behavior, as well as the consideration of the hydrodynamics of jet streams arising from the formation of fibers. Key results are presented, concerning the capillary decay of thin jets and the effect of nonlinear effects on it , leading to the formation of satellite droplets , The dynamic environment , conditions of fluid movement in the nozzle , Electromagnetic fields , heat and mass transfer on the surface and rheological complexity of the liquid (pseudoplasticity ,) dilatancy and viscoelasticity). The processes of bending of thin high-speed laminar jets moving in the air and bulging of jets and films during longitudinal compression are highlighted. Data on free turbulent jets, spraying and flattening of jets moving at very high speeds in the air are considered. When analyzing the hydrodynamic foundations of fiber and film molding processes, the main attention is paid to stability. The processes of propagation and growth of bending perturbations and perturbations of thickness on free liquid films are considered, as well as the dynamics of liquid ribs at their free edges. When presenting the results of theoretical works, quasi-one-dimensional (for jets) and quasi-two-dimensional (for films) approaches that have received comprehensive development over the past decade are singled out.