Refugees leave their country of origin under different circumstances and go to other territories in search of safety, protection, health and even survival. The health of refugees may be weakened due to the trauma faced in the country of origin, as well as the whole process of refuge and arrival in the country of destination, and it is of utmost importance that the country can adequately accommodate them. The objective of the study is to investigate how refugees have access to health and their fundamental right from the perspective of the Single Health System (SUS). The study presented is based on literature searches for available scientific publications and is qualitatively presented as a theoretical search. In Brazil, the number of refugees is growing, and the country has a public health system, which is central to universality, completeness and equity of care. This highlights the importance of having a health system that takes equal account of these people, while respecting human rights and dignity. The results show that SUS still has a lot of progress to meet everyone on equal terms, to promote improvements in health and to reduce health. It is hoped that this study will present issues that could broaden the vision of the population on the proposed topic in order to seek measures to improve the handling of refugees by the SUS in Brazil.