Since the demonstration of its involvement in cell proliferation, the eukaryotic initiation factor 5A (eIF5A) has been studied principally in relation to the development and progression of cancers in which the isoform A2 is mainly expressed. However, an increasing number of studies report that the isoform A1, which is ubiquitously expressed in normal cells, exhibits novel molecular features that reveal its new relationships between cellular functions and organ homeostasis. At a first glance, eIF5A can be regarded, among other things, as a factor implicated in the initiation of translation. Nevertheless, at least three specificities: (1) its extreme conservation between species, including plants, throughout evolution, (2) its very special and unique post-translational modification through the activating-hypusination process, and finally (3) its close relationship with the polyamine pathway, suggest that the role of eIF5A in living beings remains to be uncovered. In fact, and beyond its involvement in facilitating the translation of proteins containing polyproline residues, eIF5A is implicated in various physiological processes including ischemic tolerance, metabolic adaptation, aging, development, and immune cell differentiation. These newly discovered physiological properties open up huge opportunities in the clinic for pathologies such as, for example, the ones in which the oxygen supply is disrupted. In this latter case, organ transplantation, myocardial infarction or stroke are concerned, and the current literature defines eIF5A as a new drug target with a high level of potential benefit for patients with these diseases or injuries. Moreover, the recent use of genomic and transcriptomic association along with metadata studies also revealed the implication of eIF5A in genetic diseases. Thus, this review provides an overview of eIF5A from its molecular mechanism of action to its physiological roles and the clinical possibilities that have been recently reported in the literature.