<p>Minute amounts of long-chain flexible polymers dissolved in fluid flows can significantly alter the flow behaviors, including polymer drag reduction in wall-bounded turbulence and elastic turbulence in low Reynolds number flow. Polymer-turbulence interaction, a combination of two fields with many interacting degrees of freedom deviated far from equilibrium, is the key to understanding these intriguing phenomena. In this paper, we review the recent progress of polymer-turbulence interaction in homogeneous isotropic turbulence. For integrity, we first list the governing equations for the flow of a dilute polymer solution. Afterwards, we summarize related theories for the critical length scale below which the energy cascade of Newtonian turbulence is affected by polymers. We then review the theoretical, experimental, and numerical results about the scaling and statistical properties in those affected range of scales. We also include the implications of these results for polymer drag reduction in wall-bounded turbulence. The review has ended up with conclusions from our present understanding and outlooks for future work.</p>