Liver transplantation from living donors developed rapidly in the last decade of the twentieth century and is now an important option in the treatment of patients with end stage and/or irreversible liver diseases. Although the disadvantages of small-for-size grafts are being significantly mitigated by the repertoire of left lobe, while left liver, and right lobe grafts, the struggle for graft size matching has disclosed not a few problems, such as small grafts for advanced disease, anatomical variations in donor livers, and, above all, the increasing importance of donor safety. The range of donor candidates is also an important point of discussion in regard to the social significance of this treatment modality. Apart from the surgical aspects, many medical aspects, including the indications and timing of transplantation specific to this technique, the prevention of disease transmission in family members, and immunological aspects, including the risk of graft-versus-host disease, remain to be clarified. Social and economic questions, as well as surgical and medical issues, will be the theme in the second decade, and the new century, of this newborn treatment modality.