This review provides a synthesis of recent work, using computational methods, on the action and inhibition mechanisms of class I ribonucleotide reductase (RNR). This enzyme catalyzes the rate-limiting step of the pathway for the synthesis of DNA monomers and, therefore, has long been regarded as an important target for therapies aiming to control pathologies that depend strongly on DNA replication. In fact, over the last years, several molecules, which are able to impair RNR activity by different mechanisms, have been applied effectively in anti-cancer, anti-viral and anti-parasite therapies. A better understanding of the chemical mechanisms involved in normal catalysis and in inhibition of the enzyme is important for the rational design of more specific and effective inhibitor compounds. To achieve this goal, computational methods, particularly quantum chemical calculations, have been used more and more frequently. The ever-growing capabilities of these methods together with undeniable advantages make it a stimulating area for research purposes.