The need for studying and promoting web-archiving for longterm information preservation and accessibility in future is substantiated. The existing technologies of web-archiving are specified and the problems related to the web dynamic character, errors, content complexity, are revealed. Successful experience in the world libraries’ web-archiving is discussed (selection, search, description technologies, access terms, etc.). The study findings demonstrate that web-archives are selected to supplement the libraries’ digital collections on hot topics, like COVID-19, or to meet the demands of specific user groups. For the purpose of cultural heritage preservation, the national libraries often focus of acquiring web-sites by the domains in the corresponding country. The university libraries focus on acquiring web-archives that meet research and educational demands of their users; and public libraries prefer the resources of interest to their local community. The findings may be used by world libraries for developing their digital collections.