Flexible polymer additives are known to reduce the energy dissipation and friction drag in turbulent flows. As the fluid elasticity increases, the flow undergoes several stages of transitions. Much attention in the area has been focused on the onset of drag reduction (DR) and the eventual convergence to the maximum drag reduction (MDR) asymptote. Between the onset and MDR, recent experimental and numerical observations prompted the need to further distinguish the low- and high-extent drag reduction (LDR and HDR). Fundamental knowledge of this transition will be important for understanding turbulent dynamics in the presence of polymers, as well as for inspiring new flow control strategies for efficient friction reduction. We use direct numerical simulation (DNS) to explore all these transitions in the parameter space and, in particular, demonstrate that the LDR HDR transition is not merely a quantitative effect of the level of drag reduction, but a qualitative transition into a different stage of turbulence. A number of sharp changes in flow statistics are found to accompany the transition and at HDR, turbulence becomes localized with vortices forming clusters. These observations suggest that polymer-induced drag reduction follows two distinct stages. The first starts at the onset of drag reduction, where the coil-stretch transition of polymers causes an overall suppression of turbulent fluctuations. The second starts at the LDR HDR transition, where flow statistics become fundamentally changed in the log-law layer and turbulence localization is observed. A mechanism is then proposed for the latter based on the changing vortex regeneration dynamics between LDR and HDR.