The paper offers a review of evolution approaches to the sustainable development assessment in different world countries and in Russian practice. The research is based on the analysis of world practice assessment of sustainable development effectiveness, relevant methodologies, indicators and their modifications in modern conditions. The existing problems in developing of indicators for the sustainable state measuring of various countries with different development level are characterized. The difficulties of cross-country comparison of these indicators are highlighted. The most important aspects of sustainable development assessment, such as indicators and investments are considered. The main directions of sustainable development assessment for Russia are determined at the present stage of the national economy development.