The author examines the current problems of web-archiving practice in this country and abroad. The international standards and other important documents were retrieved and analyzed; the contextual environment (international projects and organizations) were explored, related Russian legislation is evaluated. The method of inductive information analysis was applied to analyze current publications on the subject, projects and initiatives, and websites of leading research and service organizations. The author analyses international standards in web-archiving, defines key technological problems, and discusses modern software products for copying web-documents. He also analyses the trends in webarchiving in the aspect of saving personal user accounts: allocating personal digital archives in the regional cultural web-collections. The current status of national web-archiving is analyzed as the case study of B. Yeltsin Presidential Library which mission is to preserve resources related to the powers of the state: websites of governmental organizations and agencies. This group of web-documents can be replicated without any constraints as it comprises information on executive authorities. The author suggests a selective approach toward web-archiving, i. e. replication and building collections of webdocuments on socially important events.