Within the last decade, a large number of viruses genetically related to human hepatitis viruses have been identified in different animal species, including monkeys. Numerous viruses related to human hepatitis A virus (HAV, Picornaviridae: Hepatovirus: Hepatovirus A) were detected in various mammalian species in 2015–2018, predominantly in bats and rodents, but also in shrews, seals and marsupials. Zoonotic hepatitis E virus (HEV, Hepeviridae: Orthohepevirus: Orthohepevirus A) genotypes have been found in wild boars, deer, camels, and rabbits, as well as in non human primates. In addition, viruses that are genetically close to HEV have been described in bats, ferrets, rodents, birds, and fish. Nevertheless, monkeys remain important laboratory animals in HAV and HEV research. The study of spontaneous and experimental infection in these animals is an invaluable source of information about the biology and pathogenesis of these viruses and continues to be an indispensable tool for vaccine and drug testing. The purpose of this literature review was to summarize and analyze published data on the circulation of HAV and HEV among wild and captive primates, as well as the results of experimental studies of HAV and HEV infections in monkeys.