The surface of the influenza virus is decorated with the receptor-binding protein hemagglutinin (HA) and the receptor-cleaving enzyme neuraminidase (NA). HA is responsible for host cell recognition, while NA prevents aggregation and entrapment, but the intricate mechanism of how the functions of these glycoproteins cooperate and how they are regulated by mutational responses to environmental pressures remains unclear. Recently, several groups have described the motion of influenza over surfaces and reported that this motion is inhibited by NA inhibitors. We argue that the motion of influenza resembles the motility of artificial receptor-cleaving particles called "molecular spiders". The cleaving of receptors by this type of molecular walkers leads to self-avoiding motion across a surface. When the binding and cleaving rates of molecular spiders are balanced, they move both rapidly and efficiently. The studies of molecular spiders offer new insights into the functional balance of HA and NA, but they do not address the asymmetric distribution of HA and NA on the surface of influenza. We propose that receptor-cleaving molecular walkers could play an important role in the further investigation of the motility of influenza viruses.