The robotization of industries and daily life activities had long been transformed from innovation and curiosity to reality. The use of collaborative robots (cobots) has now become widespread, capable of safely working together with a human in a single working space and increasing the efficiency of work in professions that are cannot be automated easily so far. The researchers and economists are making optimistic projections of increasing the rate of adoption of robots and cobots both in industries and in everyday human activities. However, there are difficulties and problems on the way to mass robotization, and construction of the socio-cyber-physical environment, including fear and distrust of robots, differences in the attitude towards robots in different countries and social groups, incomprehension of the relevance of robotization, etc. In addition, there are well- known problems, that are still under discussion and have no ready solutions. In this article we consider the current state of affairs in the sphere of deployment of cobots in the world and Russia, consider optimistic forecasts of the process of robotization, but also form a list of known and potential problems and negative factors, that could potentially hamper the implementation of plans for mass robotization and cobotization of industries and society, and provide our common vision of the solution of these problems.