The literature on taxation of rents from nonrenewable resources uses different theoretical assumptions and methods and a variety of empirical observations to arrive at widely diverging conclusions. Many studies use models and methods that disregard uncertainty, investigating distortionary effects of different taxes on whether, when, and how to explore for, develop, and operate resource deposits. Introducing uncertainty into the analysis opens a range of challenges and leads to results that cast doubt on the relevance of studies that neglect uncertainty. There are, however, several ways to analyze uncertainty regarding companies' behavior, resource price processes, and diversification opportunities, all with different implications for taxation. Methods developed in financial economics since the 1980s, though promising, are still not in widespread use. Additional topics covered in this review are optimal risk sharing between companies and governments, time consistency and fiscal stability, the relationship between taxes and discount rates, tax competition, and transfer pricing.