Cloud computing may be borderless, but taxes are territorial. It is easy to imagine how the two concepts can clash. Much effort has gone into harmonizing tax rules across borders with the result that many jurisdictions have very similar tax rules. Even so, taxation remains a basic expression of national sovereignty. The goal of this thesis is to examine how international tax law applies to the cross-border cloud computing business. Both, multinational providers and customers of cloud computing services are analyzed. Reflecting three traditional areas of international tax scholarship, the goal could be stated in three questions. Which jurisdictions have the right to tax? What kinds of cloud computing transactions can be taxed? What amount of the profit is taxable? In more technical terms, this means enquiring into how the use of cloud computing affects the permanent establishment status of taxpayers, how the different kinds of cloud computing transactions are characterized under international double taxation treaties, and how the calculation of taxable cloud computing profit is affected by transfer pricing. In light of the current political events, the thesis also offers recommendations de lege lata through a systematic approach. Its first part assesses the current taxation of cloud computing. The second part evaluates whether the findings of this initial assessment conform to various superior principles of good rulemaking. It identifies which of the present tax rules ought to be adapted. The final part considers how the rules could be amended to become more compliant with the superior principles. In this way, Part I embodies the thesis, Part II the antithesis, and Part III seeks a synthesis.