First part of the paper provides an overview of the factors affecting requirements and trends of modern international science and technology cooperation (ISTC). The second part discusses two modern ISTC formats: a) complex programs where different tasks are mutually reinforcing each other providing maximum satisfaction of stakeholder`s interests; b) institutionalized (based on universities and other structures) and informal (research communities) networks. Platform solutions are an integrating element: being a part of complex programs, they functionalize networks. Considering Russian ISTC it`s unsystematic nature and insufficient scale are revealed, as well as emphasis on traditional forms with limited attempts to implement modern formats. This situation is defined by organizational and institutional constraints including low involvement of the scientific and business community in the formation and implementation of ISTC, unwillingness of government to delegate authority, possibly low cooperative culture of Russian science. Some solutions for existing problems are considered.