Influenza A viruses, members of the Orthomyxoviridae family, are responsible for annual seasonal influenza epidemics and occasional global pandemics. The binding of viral coat glycoprotein hemagglutinin (HA) to sialylated glycan receptors on host epithelial cells is the critical initial step in the infection and transmission of these viruses. Scientists believe that a switch in the binding specificity of HA from Neu5Acα2-3Gal linked (α2-3) to Neu5Acα2-6Gal linked (α2-6) glycans is essential for the crossover of the viruses from avian to human hosts. However, studies have shown that the classification of glycan binding preference of HA based on sialic acid linkage alone is insufficient to establish a correlation between receptor specificity of HA and the efficient transmission of influenza A viruses. A recent study reported extensive diversity in the structure and composition of α2-6 glycans (which goes beyond the sialic acid linkage) in human upper respiratory epithelia and identified different glycan structural topologies. Biochemical examination of the multivalent HA binding to these diverse sialylated glycan structures also demonstrated that high affinity binding of HA to α2-6 glycans with a characteristic umbrella-like structural topology is critical for efficient human adaptation and human-human transmission of influenza A viruses. This review summarizes studies which suggest a new paradigm for understanding the role of the structure of sialylated glycan receptors in influenza virus pathogenesis.