It has been 20 years since functional near-infrared spectroscopy (fNIRS) was first used to investigate the evoked hemodynamic response to a stimulus in newborns. The hemodynamic response to functional activation is well-established in adults, with an observed increase in concentration change of oxygenated hemoglobin (Δ[HbO2]) and decrease in deoxygenated hemoglobin (Δ[HHb]). However, functional studies in newborns have revealed a mixed response, particularly with Δ[HHb] where an inconsistent change in direction is observed. The reason for this heterogeneity is unknown, with potential explanations arising from differing physiology in the developing brain, or differences in instrumentation or methodology. The aim of this review is to collate the findings from studies that have employed fNIRS to monitor cerebral hemodynamics in term newborn infants aged 1 day−1 month. A total of 46 eligible studies were identified; some studies investigated more than one stimulus type, resulting in a total of 51 reported results. The NIRS parameters reported varied across studies with 50/51 cases reporting Δ[HbO2], 39/51 reporting Δ[HHb], and 13/51 reporting total hemoglobin concentration Δ[HbT] (Δ[HbO2] + Δ[HHb]). However, of the 39 cases reporting Δ[HHb] in graphs or tables, only 24 studies explicitly discussed the response (i.e., direction of change) of this variable. In the studies where the fNIRS responses were discussed, 46/51 cases observed an increase in Δ[HbO2], 7/51 observed an increase or varied Δ[HHb], and 2/51 reported a varied or negative Δ[HbT]. An increase in Δ[HbO2] and decrease or no change in Δ[HHb] was observed in 15 studies. By reviewing this body of literature, we have identified that the majority of research articles reported an increase in Δ[HbO2] across various functional tasks and did not report the response of Δ[HHb]. Confirming the normal, healthy hemodynamic response in newborns will allow identification of unhealthy patterns and their association to normal neurodevelopment.