Dilute synthetic and biopolymer solutions have been shown to reduce turbulent drag in pipelines and around marine vehicles due to their viscoelasticity. The very low concentrations of polymer employed in drag reduction studies makes direct imaging of the mixing and turbulent flow structures an outstanding challenge and necessitates an experimental technique to uniquely track the evolution in the dilute polymer solution phase. In this work, we combine high speed and Schlieren imaging protocols to enable direct flow visualization of the mixing dynamics and vortical structures that develop in turbulent jets of dilute aqueous polymer solutions injected into quiescent water. At the interface of the viscoelastic jet and water, a free shear boundary layer develops leading to momentum transfer between the two fluids. We demonstrate the impact of viscoelasticity on this momentum transfer and formation of turbulent vortical structures. It is shown that under certain conditions, an increase in viscoelasticity completely eliminates the vortical structures of a turbulent resulting in re-laminarization. A comprehensive state diagram is proposed to fully characterize transition to turbulence, turbulence, and re-laminarization based on the viscoelastic properties of the jet. In this state diagram, the Reynolds number, elasticity number, and polymer viscosity ratio characterize the interaction between inertial, elastic, and viscous forces. It is shown that the elasticity number criterion suggested by Hinch and Rallison for eliminating the linear modes of instability, together with a high polymer viscosity ratio are necessary and sufficient conditions for re-laminarization. Finally, the change in the spatiotemporal structure of turbulent jets is investigated as their viscoelastic properties change. We show that the distribution of dominant mixing wave numbers over time progressively changes as the elasticity of the polymer solutions increases.