This paper presents a research survey on the Home Health Care. It is a way of caring for patients who suffer from complex, non-serious diseases and especially evolutionary ones. At their homes, they benefit from medical and paramedical cares that can be only provided by hospitals. This form of treatment has a positive impact on both the patients and the state. To study its evolution as well as its development and to understand the difference in this new mode of care, we have devoted the first part of this investigation for the home health care history. In the second part, based on official data published on the websites of the European and American States, we have analyzed home health care centers, the most recognized ones at the national and internal levels, to distinguish similarities and differences between them and especially to determine their specifications and limitations. To overcome the latter, it is necessary to dig new leads of research; that is why the founders of these institutions have resorted to scientists. The third section covers the state of the art since the 70s. In this part, we have depicted the research work that contributed to resolve home health care problems.