Unlike for pseudodifferential operators, showing even just L²-boundedness for a general Fourier Integral Operators is nontrivial. This is especially true if the corresponding canonical relation cannot be written as a graph over the cotangent bundle of the source manifold. We will have a look at a paper by Phong and Stein proving L²-boundedness for Fourier Integral Operators on R with a nondegenerate polynomial phase function.