Table 1 and Table 2 show the host ranges, diseases, receptor-binding viral spikes and receptors of influenza viruses (IVs) and coronaviruses (CoVs), respectively. According to the International Committee on Taxonomy of Viruses [117], IVs in the family Orthomyxoviridae are divided into four genera: Alphainfluenzavirus, Betainfluenzavirus, Gammainfluenzavirus and Deltainfluenzavirus (previously, Influenzavirus A, B, C and D, respectively). CoVs in the subfamily Orthocoronavirinae of the family Coronaviridae are divided into four genera: Alphacoronavirus (αCoV, previously group 1), Betacoronavirus (βCoV, previously group 2), Gammacoronavirus (γCoV, previously group 3) and Deltacoronavirus (δCoV, a new group). The genus βCoV is subdivided into four lineages: A, B, C and D. Both IVs and CoVs are enveloped single-stranded RNA viruses. However, IV genomes are negative-sense, linear RNA segments (eight segments for influenza A and B viruses and seven segments for influenza C and D viruses [86]), whereas the CoV genome is a positive-sense, linear RNA molecule [118]. Various CoVs cause a variety of diseases in mammals and birds [118]. In contrast, IVs in mammals (except for bat H17 and H18 viruses that were found in rectal swabs [119,120]) mainly cause respiratory infection [4,42], whereas infection of IVs in birds occurs in the intestinal and respiratory tracts [121,122]. The virus host range is chiefly determined by the viral spike glycoproteins carrying receptor binding sites for attachment of host receptors initiating virus infection. To bind to host receptors, influenza A viruses (IAVs) and influenza B viruses (IBVs) use hemagglutinin (HA), while influenza C viruses (ICVs) and influenza D viruses (IDVs) use hemagglutinin-esterase-fusion (HEF) to bind to host receptors as indicated in Table 1. Only IAVs have a broad range of host species. An IAV structure with HA spikes and the position of a receptor binding site (RBS) on an HA1 subunit are shown in Figure 1. Avian IAVs from wild birds are thought to be the origin of all mammalian IAVs (not known for bat H17 and H18 viruses) including all human IAVs [123]. CoVs use their spike (S) glycoproteins in N- and/or C-terminal domains of the S1 subunit, S1-NTD and/or S1-CTD, respectively, as indicated in Table 2. Specially, CoVs in lineage A of the genus βCoV have additional spike glycoproteins, hemagglutinin-esterases (HEs), possibly acquired from influenza C virus (ICV) during mixed infection [124]. A CoV structure with S and HE spikes and positions of S1-NTD and S1-CTD on the S spike are shown in Figure 2. Bat CoVs are likely to be the ancestral origins of two seasonal αCoVs, HCoV-229E [125,126] and HCoV-NL63 [127], two zoonotic lineage B and lineage C βCoVs, SARS-CoV (which has disappeared in humans) [128,129,130] and MERS-CoV [108,131], respectively, and an ongoing pandemic lineage B βCoV, SARS-CoV-2 [132,133]. Rodent CoVs are likely to be the ancestral origins of two seasonal lineage A βCoVs, HCoV-OC43 and HCoV-HKU1 [85]. So far, γCoVs and δCoVs have been mainly found in birds [85]. This review will focus on human viruses and potential zoonotic viruses and the main spike glycoproteins determining host-specific virus infection.