This paper discusses and fosters concerns in light of the repercussions of both the 40th anniversary of the Alma-Ata Declaration and the Astana Declaration, discussing the possible influence on Family and Community Medicine training, as per the lenses of two Residency Programs of three public institutions, namely, State University of Rio de Janeiro, Federal University of Rio de Janeiro, and the Oswaldo Cruz Foundation. These are inserted in a historical and social context, between the world of work, public policies, international organizations, the population and subjects involved in the construction, maintenance, and consolidation of the Brazilian PHC. Thus, in a brief historical revival, we contextualized which Primary Care was a practice setting and where we might be headed. We concluded that the willingness to ensure the Right to Health would be threatened by the concept of Universal Coverage, advocated by the Astana Declaration, which leads to essential discussions: ensuring state-provided services, advocating for equity and integrality of actions, reaffirming the risk of generating inequality by creating multiple service offerings for different segments of the population, reiterating the relevance of access to health, and valuation of territorialization.