The iron-based superconductors, discovered a few years ago, hold a great promise, from both a technological and a scientific point of view. With an unusually high maximum critical temperature exceeding 50K, second only to that of the so-called copper-oxide high-temperature superconductors, they are likely to belong to a class of "unconventional" superconductors, whose mechanism lies beyond the Bardeen-Cooper-Schrieffer theory of phonon-mediated pairing. A crucial step to unveil the mechanism of superconductivity in these materials is to understand the structure of their order parameter. In this talk, I will discuss theoretical investigations of the iron-based superconductors, which indicate an exotic order parameter with an internal sign change. Experimentally, detecting such a sign change poses a significant challenge. I will show how a recent intriguing experiment, which shows fractional flux quantization in a composite superconducting loop, can be intepreted as evidence for a sign-changing order parameter.