This paper gives a survey on the Constitutional Law (Treaty Law) of the European Union from a Public Choice perspective. The focus is on the impact of alternative voting rules within the Council, and on the strategic interaction between the institutions of the Community (Council, Commission, European Parliament, European Court of Justice). In addition, we give an overview of the most important open questions and problems of the EU Constitution, which are expected to come up in the negotiations about future treaty amendments in the Council, as well as in the newly created Convention on the Future of Europe.