Despite the development of efficient vaccines, the impact of the COVID-19 pandemic around the world, caused by the novel severe acute respiratory syndrome coronavirus-2 -SARS-CoV-2 -has emphasized the need for effective antiviral treatments. Moreover, considering the capabilities of the virus to mutate, as any other viruses that contain RNA genetic material such as this or the influenza viruses, the corresponding risk of a decrease of the effectiveness of the vaccines urged the need of complementary strategies to fight against the pandemia. Many efforts have focused on understanding the life cycle of SARS-CoV-2, which can provide information about possible targets for drug development. Among the proteins involved in the replication of the virus, the main coronavirus protease (SARS-CoV-2 M pro ) is a most attractive target due to its intrinsic features, including its distinguishing ability with respect to human proteases to cleave proteins after glutamine residue, a catalytic features which makes M pro unique with respect to human proteases. The most effective M pro inhibitors so far identified, including the clinical candidates PF-00835231, incorporate a glutamine residue or a bioisostere at P1 position (see below) to obtain potency and selectivity and a peptidomimetic scaffold of moderate size endowed with branched and yet hydrophobic substituents at both P2 and P3 positions. These compounds act by a covalent-based mechanism, so a reactive 'warhead' is required, i.e. an electrophilic group responsible for the covalent bond formation between the active site cysteine residue (Cys145), previously activated by a histidine residue (His41), and the inhibitor. Warheads so far employed ranged from classical Michael acceptors (MAs) to activated carbonyl derivatives, including alphaketoamides, aldehydes and hydroxymethylketone (HMK). Nevertheless, previous studies of the inhibition of M pro do not show which is the most reactive warhead to design an efficient inhibitor, nor which is the most appropriate recognition part to increase the affinity of the inhibitor by the enzyme active site. Thus, there is a need to understand the effects of warheads on reactivity and e.g. reversibility of inhibitors, which may significantly affect their pharmacokinetics. A plethora of different computational methods have used since the emergence of COVID-19 for the discovery of smallmolecule therapeutics. Regarding the inhibition of M pro , modelling can contribute effectively to noncovalent inhibitor development, while the use of methods based on multiscale quantum mechanics/molecular mechanics (QM/MM) potentials can help with covalent inhibitor design. We recently studied the mechanism of the covalent inhibition of the peptidyl-MA compound N3 designed by Jin and colleagues, and two designed MA compounds (B1 and B2) by QM/MM molecular dynamics (MD) methods. Our results indicated that both designed compounds may be promising candidates as drug leads against COVID-19, one as an irreversible inhibitor and one as a potential reversible inhibitor.