Opinions are divided on the impact of population aging on healthcare costs. Some argue that demographic trends over the coming decades will be unsustainable for public finances and will inevitably undermine the health insurance system. Others, however, contend that aging will ultimately have only a limited and very manageable impact on healthcare spending. This second viewpoint is supported by a significant portion of the scientific community (as aptly summarized by the tongue-in-cheek title of a paper on this subject by Robert Evans, a Canadian health economist: “Apocalypse No”), while stakeholders in the healthcare system and the media hold a more pessimistic outlook. To shed light on this divergence of views, this literature review summarizes the current state of knowledge and identifies the uncertainties, points of debate, and unresolved questions that future research must address.