Influenza viruses belong to the family Orthomyxoviridae with a negative-sense, single-stranded segmented RNA genome. They infect a wide range of animals, including humans. From 1918 to 2009, there were four influenza pandemics, which caused millions of casualties. Frequent spillover of animal influenza viruses to humans with or without intermediate hosts poses a serious zoonotic and pandemic threat. The current SARS-CoV-2 pandemic overshadowed the high risk raised by animal influenza viruses, but highlighted the role of wildlife as a reservoir for pandemic viruses. In this review, we summarize the occurrence of animal influenza virus in humans and describe potential mixing vessel or intermediate hosts for zoonotic influenza viruses. While several animal influenza viruses possess a high zoonotic risk (e.g., avian and swine influenza viruses), others are of low to negligible zoonotic potential (e.g., equine, canine, bat and bovine influenza viruses). Transmission can occur directly from animals, particularly poultry and swine, to humans or through reassortant viruses in "mixing vessel" hosts. To date, there are less than 3000 confirmed human infections with avian-origin viruses and less than 7000 subclinical infections documented. Likewise, only a few hundreds of confirmed human cases caused by swine influenza viruses have been reported. Pigs are the historic mixing vessel host for the generation of zoonotic influenza viruses due to the expression of both avian-type and human-type receptors. Nevertheless, there are a number of hosts which carry both types of receptors and can act as a potential mixing vessel host. High vigilance is warranted to prevent the next pandemic caused by animal influenza viruses.