Understanding how influenza viruses traverse the mucus and recognize host cells is critical for evaluating their zoonotic potential, and for prevention and treatment of the disease. The surface of the influenza A virus is covered with the receptor-binding protein hemagglutinin and the receptor-cleaving enzyme neuraminidase, which jointly control the interactions between the virus and the host cell. These proteins are organized in closely spaced trimers and tetramers to facilitate multivalent interactions with sialic acid-terminated glycans. This review shows that the individually weak multivalent interactions of influenza viruses allow superselective binding, virus-induced recruitment of receptors, and the formation of dynamic complexes that facilitate molecular walking. Techniques to measure the avidity and receptor specificity of influenza viruses are reviewed, and the pivotal role of multivalent interactions with their emergent properties in crossing the mucus and entering host cells is discussed. A model is proposed for the initiation of cell entry through virus-induced receptor clustering. The multivalent interactions of influenza viruses are maintained in a dynamic regime by a functional balance between binding and cleaving.