Dominant or apparently dominant internet platform increasingly become subject to both antitrust investigations and further-reaching political calls for regulation. While Google is currently in the focus of the discussion, the next candidate is already on the horizon - the ubiquitous online trading platform Amazon. Competitors and suppliers but also famous economists like Paul Krugman unite in criticizing Amazon's market power and alleged abuse of it. In this paper, we collect the multitude of allegations against Amazon and categorize them according to types of potential anticompetitive conduct or types of market failure. We provide an economic analysis of these allegations based upon economic theory as well as publicly available information and data. As one of our main results, we find that the most severe allegations against Amazon do not hold from an economic perspective and, consequently, do not warrant regulation or other drastic interventions (like breaking the company up). However, several areas of conduct, in particular, the use of best price clauses and the (anti-) competitive interplay of Amazon and the major publishers in the e-book market require competition policy action. The standard antitrust instruments, enriched with modern economic theory, should suffice to disincentivize the identified anticompetitive conduct for now.