The post-industrial society is transforming into a smart society, in which smart technologies control all the main processes. The study aims at proposing indicators for assessing the spread of smart technologies in various spheres of human life with due regard to the introduction of open innovations. The methodological basis of the study was an approach focused on the study of the processes of development of open innovations and the smartization of society with the involvement of special methods. Special methods include document analysis based on a literature review conducted by the authors, content analysis using multiple correspondence analysis and the cluster analysis method. This is the first study to use the Smart Progress Index like other social development indices, including the Social Progress Index, the Physical Quality Life Index and the Sustainable Economic Welfare Index. The Smart Progress Index will determine the state of society and the level of its development in technological, geopolitical, socio-economic, demographic and environmental terms. There are three indicators of the Smart Progress Index: 1) the scale of smart technologies; 2) the conditions and intensity of introducing smart technologies; 3) the results of smart technologies. Each aspect includes several components represented by seventeen indicators.