In the present paper the authors consider technological and legal problems that arise in the course of adopting information technology in legal proceedings. The authors analyze the efficiency of using digital technologies in the administration of justice within the crisis period of 2020 on the basis of the World Justice Project, worked out by the Council of European Commission for the Efficiency of Justice CEPEJ. These technologies are used by both courts of the Russian Federation and courts of some other countries. The paper presents the analysis of prospects to apply artificial intelligence in the work of courts during adjudication on certain categories of disputes (issuance of a court order, consideration of cases as summary judgment proceedings). In order to ensure accessibility of justice, the authors urge on necessity to turn to online legal proceedings; they also highlight the necessity to organize special legal services for individuals (free-of-charge) and for business entities. The paper calls for the urgency to create a special digital portal for pretrial settlement of disputes between legal entities.