The aim of the present study is to consider a range of problems that are to be solved during the implementation of projects that are aimed at increasing the access to healthcare and based on the achievements of the new technological order on the example of Latvia, primarily the e-health project. Since January 1, 2018, the use of the e-health system in Latvia is mandatory, but so far only the “Digital Prescription (e-prescription)” project has been functioning at full capacity. The experience with the introduction and use of digital medicine in Latvia indicates a large range of problems faced by state institutions and local self-government institutions, medical establishments, medical personnel, and patients. A systematic vision of the problems of implementing digital medicine requires a necessity at least to take into account and solve seven relatively independent tasks: technical and technological, economic, legal, organizational, managerial, social, psychological, and cultural ones. In terms of systemic vision, the assessment of these aspects of the e-health programme implementation is presented by means of an extensive use of data retrieved from international organizations, Latvian state statistics, scientific research studies, including the ones carried out by the authors. The main conclusion of the study is the need for the theory and the practice of the increasing access to healthcare based on digital medicine, taking into account a more complete variety of factors that stimulate and constrain this process, and involving specialists from the sphere of social sciences.