Copper or iron-based ATRP (atom transfer radical polymerization) catalytic systems with various ligands are among most efficient controlled/living radical polymerization systems. By applying new initiating/catalytic systems, transition metal level in ATRP was reduced to a few ppm. The activators are regenerated by light, reducing agents, electrical current or mechanical forces. By employing these systems, ATRP of acrylates, methacrylates, styrenes, acrylamides, acrylonitrile and other vinyl monomers was employed for macromolecular engineering of polymers with precisely controlled molecular weights, tuned dispersities, designed shape, composition and functionality. These polymers form nanostructured multifunctional materials for application related to biomedicine, environment, energy, catalysis and other advanced technologies.