The paper presents a review of key publications on Transdisciplinarity (TD), the science and the methodology which active contemporary development is caused by growth of human activity in planetary scales (challenges of the Anthropocen). The review has revealed an eclectic enough collection of projects and new structures created mainly for the task of solving of problems of modern socio-economic development and integrative/transdisciplinary education. At the same time, some concrete projects of development of organizational forms and examples of convergence of socially demanded knowledge, appear rather actual. The paper mainly considers the sources that describe the following TD aspects: genesis (from antiquity up to now; conflicts and struggle of interests), ontology (Levels of Reality, their relations with levels of TD), epistemology (criteria of truth, the types of logic, new modes of education), political economy (a science as a form of public work organization) and ethical appliances (a "regulating ideal" thematic, ethical aspects of scientific research). Following the results of the review the author concludes that TD, presumably, is ready to support that direction of socio-economic, civilizational developments which will be supported by resources of stakeholders. The spectrum of possible basic methodological assumptions of the chosen direction can be wide enough: from "moist robot" to "builder of the lucid future with strong spirit". TD does not aspire to create a general theoretical structure, but, appeals of a wider reflexivity, including - "humility", openness for interaction with others methodologies and experts, contextualization of one's own knowledge and readiness to give way to other approaches if they are more adequate to modern challenges.