The neuraminidase (NA) of influenza A and B viruses plays a distinct role in viral replication and has a highly conserved catalytic site. Numerous sialic (neuraminic) acid analogs that competitively bind to the NA active site and potently inhibit enzyme activity have been synthesized and tested. Four NA inhibitors are now licensed in various parts of the world (zanamivir, oseltamivir, peramivir, and laninamivir) to treat influenza A and B infections. NA changes, naturally occurring or acquired under selective pressure, have been shown to reduce drug binding, thereby affecting the effectiveness of NA inhibitors. Drug resistance and other drawbacks have prompted the search for the next-generation NA-targeting therapeutics. One of the promising approaches is the identification of monoclonal antibodies (mAbs) targeting the conserved NA epitopes. Anti-NA mAbs demonstrate Fab-based antiviral activity supplemented with Fc-mediated immune effector functions. Antiviral Fc-conjugates offer another cutting-edge strategy that is based on a multimodal mechanism of action. These novel antiviral agents are composed of a small-molecule NA inhibitor and an Fc-region that simultaneously engages the immune system. The significant advancements made in recent years further support the value of NA as an attractive target for the antiviral development.