The enormous development of genomics research in recent decades has raised great expectations concerning its impact on biomedicine. There has been growing investment in research in personalized or precision medicine, which aims to customize medical practice with a focus on the individual, based on the use of genetic tests, identification of biomarkers, and development of targeted drugs. However, the personalized or precision medicine movement is controversial and has sparked an important debate between its defenders and critics. This essay aims to discuss the assumptions, promises, limits, and possibilities of personalized or precision medicine based on a review of the recent literature situating the debate on the theme. The review indicates that many of the promises of personalized or precision medicine remain unfulfilled. While there has been huge progress in knowledge on the molecular mechanisms of diseases and the development of drugs that have significantly impacted the treatment of some types of cancer, thus far there is no evidence that this same pattern will be reproduced in other complex diseases. Personalized or precision medicine is expected to generate incremental developments in specific areas of medicine, but there are obstacles to its generalization. The high cost of new biotechnologies can exacerbate health inequalities and become a problem for health services' sustainability, especially in low and middle-income countries. The emphasis on personalized or precision medicine may shift funds away from less costly interventions that have greater public health impact.