Diseases of the preterm newborn such as bronchopulmonary dysplasia, necrotizing enterocolitis, cerebral palsy, and hypoxic-ischemic encephalopathy continue to be major causes of infant mortality and long-term morbidity. Effective therapies for the prevention or treatment for these conditions are still lacking as recent clinical trials have shown modest or no benefit. Stem cell therapy is rapidly emerging as a novel therapeutic tool for several neonatal diseases with encouraging pre-clinical results that hold promise for clinical translation. However, there are a number of unanswered questions and facets to the development of stem cell therapy as a clinical intervention. There is much work to be done to fully elucidate the mechanisms by which stem cell therapy is effective (e.g., anti-inflammatory versus pro-angiogenic), identifying important paracrine mediators, and determining the timing and type of therapy (e.g., cellular versus secretomes), as well as patient characteristics that are ideal. Importantly, the interaction between stem cell therapy and current, standard-of-care interventions is nearly completely unknown. In this review, we will focus predominantly on the use of mesenchymal stromal cells for neonatal diseases, highlighting the promises and challenges in clinical translation towards preventing neonatal diseases in the 21st century.