This article provides a review of the recent progress in understanding and predicting additives-induced drag reduction (DR) in turbulent wall-bounded shear flows. We focus on the reduction in friction losses by the dilute addition of high-molecular weight polymers and/or fibers to flowing liquids. Although it has long been reasoned that the dynamical interactions between polymers/fibers and turbulence are responsible for DR, it was not until recently that progress was made in elucidating these interactions in detail. Advancements come largely from numerical simulations of viscoelastic turbulence and detailed measurements in turbulent flows of polymer/fiber solutions. Their impact on current understanding of the mechanics and prediction of DR is discussed, and perspectives for further advancement of knowledge are provided.