The third trimester of pregnancy represents a sensitive phase for infant brain plasticity when a series of fast-developing cellular events (synaptogenesis, neuronal migration, and myelination) regulates the development of neural circuits. Throughout this dynamic period of growth and development, the human brain is susceptible to stress. Preterm infants are born with an immature brain and are, while admitted to the neonatal intensive care unit, precociously exposed to stressful procedures. Postnatal stress may contribute to altered programming of the brain, including key systems such as the hypothalamic–pituitary–adrenal axis and the autonomic nervous system. These neurobiological systems are promising markers for the etiology of several affective and social psychopathologies. As preterm birth interferes with early development of stress-regulatory systems, early interventions might strengthen resilience factors and might help reduce the detrimental effects of chronic stress exposure. Here we will review the impact of stress following premature birth on the programming of neurobiological systems and discuss possible stress-related neural circuits and pathways involved in resilience and vulnerability. Finally, we discuss opportunities for early intervention and future studies.