The paper reviews problems of the social well-being phenomenon research. It presents different approaches to interpretation of the term (ethical and philosophical, socio political, economic, psychological, medical, ecological, and social approaches). The authors make a point that term "wellbeing" is bipolar, its understanding stretches from unwellness sick to such positive feeling as happiness and enthusiasm. We review well-being components obtained during the research held in Gallup Institute (professional well-being, financial well-being, well-being in the living environment). The work also considers reasons for increase in the number of research on social well-being at the contemporary stage. Emphasis is placed upon the worldview component of social well-being. The pedagogical problem for study of the courses "Social Well-being" and "Modern Theories of Social Well-being" is outlined. Social indicators issues are reviewed as major tools for diagnostics of the state of a complex, multidimensional, dynamic society and a variety of social processes and conditions. The issue of a social well-being subjective aspect is addressed. Social indicators are viewed as main tools to diagnose complex, multidimensional, dynamic society, variety of social processes and phenomenon.