Among the four genera of influenza viruses (IVs) and the four genera of coronaviruses (CoVs), zoonotic αIV and βCoV have occasionally caused airborne epidemic outbreaks in humans, who are immunologically naïve, and the outbreaks have resulted in high fatality rates as well as social and economic disruption and losses. The most devasting influenza A virus (IAV) in αIV, pandemic H1N1 in 1918, which caused at least 40 million deaths from about 500 million cases of infection, was the first recorded emergence of IAVs in humans. Usually, a novel human-adapted virus replaces the preexisting human-adapted virus. Interestingly, two IAV subtypes, A/H3N2/1968 and A/H1N1/2009 variants, and two lineages of influenza B viruses (IBV) in βIV, B/Yamagata and B/Victoria lineage-like viruses, remain seasonally detectable in humans. Both influenza C viruses (ICVs) in γIV and four human CoVs, HCoV-229E and HCoV-NL63 in αCoV and HCoV-OC43 and HCoV-HKU1 in βCoV, usually cause mild respiratory infections. Much attention has been given to CoVs since the global epidemic outbreaks of βSARS-CoV in 2002–2004 and βMERS-CoV from 2012 to present. βSARS-CoV-2, which is causing the ongoing COVID-19 pandemic that has resulted in 890,392 deaths from about 27 million cases of infection as of 8 September 2020, has provoked worldwide investigations of CoVs. With the aim of developing efficient strategies for controlling virus outbreaks and recurrences of seasonal virus variants, here we overview the structures, diversities, host ranges and host receptors of all IVs and CoVs and critically review current knowledge of receptor binding specificity of spike glycoproteins, which mediates infection, of IVs and of zoonotic, pandemic and seasonal CoVs.