Purine and pyrimidine nucleoside phosphorylases catalyze the reversible phosphorolytic cleavage of the glycosidic bond of purine and pyrimidine nucleosides, and are key enzymes of the nucleoside salvage pathway. This metabolic route is the less costly alternative to the de novo synthesis of nucleosides and nucleotides, supplying cells with these important building blocks. Interest in nucleoside phosphorylases is not only due to their important role in metabolism of nucleosides and nucleotides, but also due to the potential medical use of the enzymes (all phosphorylases in activating prodrugs - nucleoside and nucleic base analogs, high-molecular mass purine nucleoside phosphorylases in gene therapy of some solid tumors) and their inhibitors (as selective immunosuppressive, anticancer and antiparasitic agents, and preventing inactivation of other nucleoside drugs). Phosphorylases are also convenient tools for efficient enzymatic synthesis of otherwise inaccessible nucleoside analogues. In this paper the contribution of Professor David Shugar and some of his colleagues and coworkers in studies of these remarkable enzymes carried out over nearly 40 years is discussed on the background of global research in this field.