One of the fields of medicine that has raised the most expectations in recent years is cell therapy with stem cells. The isolation of human embryo cells, the apparent and unexpected potentiality of adult stem cells and the development of gene therapy lead us to imagine a hopeful future for a significant number of diseases that are at present incurable. In this article we will sketch out the panorama of stem cell research, describing the main achievements in this field as well as some of the questions that await an answer. In spite of the great expectations, it is essential that we maintain a critical and realistic spirit when it comes to analysing the scientific advances in this area.