The promise of the new "stem cell" biology is that it is hoped that one day these cells might be used to replaced parts of human body lost through injury or disease. It may be possible for humans to grow new parts, just as lizards grow new tails or amphibians, new legs. Transplanting bone marrow stem cells to replace those lost in cancer therapy is already clinical practise and clinical trials are underway to repair the heart using these cells. The creations of new pancreatic cells for diabetes is under intensive research in animal studies, and treatments for brain diseases such as Parkinson's disease and Alzheimer's disease are though possible. These development in biotechnology promise great advances in human ailments, but at the same time raise challenging ethical dilemmas for society. In this paper some of the terminology of stem cell is presented and the biology of these cells is introduced. The focus here is therefore not on the ethical issues explicitly but rather presents the scientific background to a debate on the ethics of this exciting and rapidly advancing science. In particular this chapter introduces the concepts of "embryonic and adult stem cells" and their therapeutics potential, both dreamed of and currently embodied.