One of the fields of medicine that has created the greatest expectations in recent years is cellular therapy with stem cells. The isolation of human embryo cells, the apparent and unexpected potential 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 the following pages we offer a sketch of the panorama of research with stem cells, describing the main achievements in this field as well as some of the questions awaiting answers. 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.