In 2017, disruptions in the global supply of helium reminded consumers, distributors, and policy makers that the global helium supply chain lacks flexibility, and that attempts to increase production from the U.S. Federal Helium Reserve (the FHR) may not be able to compensate for the loss of one of the few major producers in the world. Issues with U.S. and global markets for helium include inelastic demand, economic availability of helium only as a byproduct, only 4–5 major producers, helium’s propensity to escape earth’s crust, an ongoing absence of storage facilities comparable to the FHR, and a lack of consequences for the venting of helium. The complex combination of these economic, physical, and regulatory issues is unique to helium, and determining helium’s practical availability goes far beyond estimating the technically accessible volume of underground resources. Although most of these issues have been analyzed since helium was recognized to be a valuable mineral commodity in the early 1900s, very few economic models have been developed that adequately consider the unique characteristics of helium and helium markets. In particular, there is a notable lack of recent empirical work to estimate the responsiveness of helium demand, supply, prices, and trade patterns to the ongoing drawdown and sale of helium reserves stored in the FHR. In general, existing models of helium either do not account for an oligopoly controlling supply, or they do not evaluate potential helium extraction and storage programs based on an intertemporal maximization of the value of the resource. Such models could be of very limited use to decision makers. This review found only one working paper with a helium market model that has incorporated both of these vital considerations. That and other economic studies along similar lines could be very useful in helping inform current helium policy discussions and decisions.