With the development and progress of medical technology, the survival rate of premature and low-birth-weight infants has increased, as has the incidence of a variety of neonatal diseases, such as hypoxic–ischemic encephalopathy, intraventricular hemorrhage, bronchopulmonary dysplasia, necrotizing enterocolitis, and retinopathy of prematurity. These diseases cause severe health conditions with poor prognoses, and existing control methods are ineffective for such diseases. Stem cells are a special type of cells with self-renewal and differentiation potential, and their mechanisms mainly include anti-inflammatory and anti-apoptotic properties, reducing oxidative stress, and boosting regeneration. Their paracrine effects can affect the microenvironment in which they survive, thereby affecting the biological characteristics of other cells. Due to their unique abilities, stem cells have been used in treating various diseases. Therefore, stem cell therapy may open up the possibility of treating such neonatal diseases. This review summarizes the research progress on stem cells and exosomes derived from stem cells in neonatal refractory diseases to provide new insights for most researchers and clinicians regarding future treatments. In addition, the current challenges and perspectives in stem cell therapy are discussed.