The report provides a review of research ideas about children's mobility in the environment of technological infrastructure of a smart city. Development of monitoring and surveillance systems is defined by researchers as the basis of existence of a smart city and children as particular group of smart technology users. The topic of children's mobility appeared in the 1970s when trends for reduction of independent children's mobility and an increase of children's journeys in a car found themselves. First, the authors examine ideas about contemporary everyday life family mobility that is connected with plasticity of family groups (separation of spouses, lone parenthood, guest marriage, etc.). Second, we present the development of issues of children's mobility by parent's car. Today the term "generation of backseat passengers" is popular among social scientists as a marker of modern children lifestyle. Finally, the report introduces the research ideas about social effects of children's mobility that is controlled with the help of special smartphone applications. Current studies of children's mobility focus on the social consequences of the reduction of independent movements, among them the loss of ability to spatial orientation, limiting the cognitive skills and abilities to see dangerous and safe routes.