The article analyzes approaches to assessing the sustainability of regional economic systems, taking into account their ecological subsystem. Definitions of the regional economic system and sustainability are given, approaches to assessing sustainability are considered. The absence of a unified methodology for calculating, composition and structure of criteria for assessing sustainability has been established, and it has been determined that the approach of developing indices and indicators of sustainability is most often used in assessing the sustainability of regional economic systems. The approaches to the development of indices and indicators within the framework of the concept of sustainable development, ESG indicators of sustainability, and the ESG ranking methodology are studied. The underestimation of the ecological subsystem of regional economic systems in assessing their sustainability in all the considered approaches has been revealed. The ecological component is considered either as a resource component or as an assimilation potential, the environment-forming functions of the environment, as a rule, are not taken into account. At the same time, the risks of emergency situations, real and potential economic and social damage from the development of adverse natural processes and phenomena are currently becoming limiting factors for the sustainability of regions. The use of a multicriteria (integral) approach in assessing the sustainability of regions will allow taking into account these risks.