This article presents an overview of the nature, functions and history of health surveillance in the structure of the Brazilian Unified Health System (SUS). Bibliographical sources and official documents were used, with references from the careers of the authors, who have worked in health surveillance. Extremely serious adverse events in the mid-1990s gave political visibility to the fragility of Brazilian health surveillance, and were reflected in serious problems for the SUS. The creation of Anvisa and the SNVS surveillance system, and the support for bodies in individual states and municipalities, resulted in improvement in the structure and functioning of health surveillance, and improved recognition of the area as an emerging theme in research and education in public health. Several problems hamper the effective structuring of the SNVS. A change in the conception/design of health promotion is postulated, in which the large corporations, whose activities have strong connections with risk factors related to the current epidemic of chronic diseases, would be given a social responsibility. A set of challenges for better structuring of health surveillance in the SUS is also put forward.