In the 40th anniversary, we restate the commitments of the Alma Ata Declaration with social justice, health for all, and the overcome of social inequalities between countries and intracountries. Our 40 years led to undeniable advances on health rights; however, new challenges are evidenced with the persistence of inequalities, demographic and epidemiological changes, technological transformations, and environmental and climate threats. Under the inspiration of Alma Ata, the Brazilian Federal Constitution of 1988 recognizes the connection between economic and social development and environmental conditions to determine the health-disease process and to promote health. It provides for "health as a right of all and a duty of the State" through the creation of a universal health system, the Brazilian Unified Health System (SUS), which complies with the universality, integrality, equality, and social participation for 30 years. In the Brazilian experience, primary health care is the heart of the universal health system. The care model of the Family Health Strategy with 41 thousand multidisciplinary professional teams now attends 130 million Brazilians. Universal health systems founded in a comprehensive PHC, such as the SUS, include individual care and collective actions for promotion and prevention, cure, and rehabilitation. They ensure the continuity of care coordinated by the PHC by providing access to secondary and tertiary specialized and hospital care, as needed. Their populational focus requires the promotion of intersectoral transversal public policies to cope with social and environmental determinants of health. Over three decades of SUS provided experience with their relevant impacts in improved access and people health, allowing us to elaborate the following proposals: The social determination of health and disease stated by the Alma Ata has become the hegemonic conception and requires the political commitment of governments to ensure maximum egalitarian welfare for citizens. The downturn in social policies following the economic austerity programs has been an unbearable burden for societies, mainly in the periphery countries, with increased poverty and inequalities, worse health conditions, corrosion of social cohesion, and authoritarianism threats. The PHC subsumption to the proposal of universal health coverage (UHC) restricts the possibilities to guarantee the human right to health, as defined in the Alma Ata.