Tissue fibrosis is characterized by excessive deposition of extracellular matrix (ECM) components that result from the disruption of regulatory processes responsible for ECM synthesis, deposition, and remodeling. Fibrosis develops in response to a trigger or injury and can occur in nearly all organs of the body. Thus, fibrosis leads to severe pathological conditions that disrupt organ architecture and cause loss of function. It has been estimated that severe fibrotic disorders are responsible for up to one-third of deaths worldwide. Although intensive research on the development of new strategies for fibrosis treatment has been carried out, therapeutic approaches remain limited. Since stem cells, especially mesenchymal stem cells (MSCs), show remarkable self-renewal, differentiation, and immunomodulatory capacity, they have been intensively tested in preclinical studies and clinical trials as a potential tool to slow down the progression of fibrosis and improve the quality of life of patients with fibrotic disorders. In this review, we summarize in vitro studies, preclinical studies performed on animal models of human fibrotic diseases, and recent clinical trials on the efficacy of allogeneic and autologous stem cell applications in severe types of fibrosis that develop in lungs, liver, heart, kidney, uterus, and skin. Although the results of the studies seem to be encouraging, there are many aspects of cell-based therapy, including the cell source, dose, administration route and frequency, timing of delivery, and long-term safety, that remain open areas for future investigation. We also discuss the contemporary status, challenges, and future perspectives of stem cell transplantation for therapeutic options in fibrotic diseases as well as we present recent patents for stem cell-based therapies in organ fibrosis.