The article is devoted to the analysis of the main aspects of the development of the world space activities: the growth of the space economy; an increase in the number of space activities subjects (both in the country aspect and in the functional aspects, such as the state, the private sector, public-private partnership). The impact of the space activities on the development of other sectors of the economy is emphasized. Particular emphasis of this conducted research is on the American space activities. The spiral-evolutionary approach to the development of space activities is discussed. The most important key space technologies both in terms of the development of space-based facilities and systems and the space production complex and also the main approaches of the leading space countries to the development of the space weapons are determined by the authors. In total identified aspects underline the necessity for the extension of the discussion platforms for the activating debates concerning determination of the prospects for the development of the world space activity.