The historical and cultural theory of activity is a living theory, which has been developed since the 1920s and 1930s and seeks to understand human training in social activity. Theory is becoming pari passu with the changes in the cultural contexts of theoretical and practical research using it, thus presenting changes and continuity of ideas throughout its development. In this sense, some students define three generations of Theoria, each represented by an exponent in the field of research: the first by Vygotsky (founder), the second by Leontiev and the third by Engeström. The aim of this article is to present the theoretical proposals of the three authors, outlining the relationship between them and providing an overview of the historical and cultural theory of the activity. The concept of activity, which in Vygotsky appears as a mediated activity (mediated by acrons and tools), in Leontiev as a collective activity, a basis for human consciousness, and in Engeström appears as a system of activity in processing. The production and expansion of theory can be understood as historical and collective activities.