Neonatal encephalopathy linked to hypoxia-ischemia (H-I) which is regarded as the most important neurological problem of the newborn, can lead to a spectrum of adverse neurodevelopmental outcomes such as cerebral palsy, epilepsy, hyperactivity, cognitive impairment and learning difficulties. There have been numerous reviews that have focused on the epidemiology, diagnosis and treatment of neonatal H-I; however, a topic that is less often considered is the extent to which the injury might worsen over time, which is the focus of this review. Similarly, there have been numerous reviews that have focused on mechanisms that contribute to the acute or subacute injury; however, there is a tertiary phase of recovery that can be defined by cellular and molecular changes that occur many weeks and months after brain injury and this topic has not been the focus of any review for over a decade. Therefore, in this article we review both the clinical and pre-clinical data that show that tertiary neurodegeneration is a significant contributor to the final outcome, especially after mild to moderate injuries. We discuss the contributing roles of apoptosis, necroptosis, autophagy, protein homeostasis, inflammation, microgliosis and astrogliosis. We also review the limited number of studies that have shown that significant neuroprotection and preservation of neurological function can be achieved administering drugs during the period of tertiary neurodegeneration. As the tertiary phase of neurodegeneration is a stage when interventions are eminently feasible, it is our hope that this review will stimulate a new focus on this stage of recovery towards the goal of producing new treatment options for neonatal hypoxic-ischemic encephalopathy.