The chapter deals with trends of educational processes and learning environments in post-industrial society. A historicist approach is used for this purpose. This approach is based on two theoretical recourses: analysis of historical forms of acquiring knowledge and analysis of historical forms of educational processes. The authors show that the contemporary educational process is greatly affected by two innovative phenomena: social media and personal identity online (PIO). They consider socialization and personalization as two unique entities having opposite characteristics of the post-industrial educational process. Based on such a dialectic approach to the educational process, they define the concept "Personal Ubiquitous Educational Environment". The authors report the preliminary results of research on a teachers' training course conducted on the basis of such an environment. The research focuses on clarifying both innovative components of contemporary educational processes: social media and PIO.