Over the past 15 years, functional near-infrared spectroscopy (fNIRS) has emerged as a powerful technology for studying the developing brain. Diffuse optical tomography (DOT) is an extension of fNIRS that combines hemodynamic information from dense optical sensor arrays over a wide field of view. Using image reconstruction techniques, DOT can provide images of the hemodynamic correlates to neural function that are comparable to those produced by functional magnetic resonance imaging. This review article explains the principles of DOT, and highlights the growing literature on the use of DOT in the study of healthy development of the infant brain, and the study of novel pathophysiology in infants with brain injury. Current challenges, particularly around instrumentation and image reconstruction, will be discussed, as will the future of this growing field, with particular focus on whole-brain, time-resolved DOT.