The double-slit experiment and its outcome has played a profound role in the developments of optics and quantum mechanics and has been used since as a paradigm to unveil the wave nature of a number of physical entities, in particular single electrons, neutrons, atoms and molecules. This doctoral thesis is concerned with experimental results of single and double-slit experiments in so called microwave billiards. These are electromagnetic resonators which enable the investigation of chaotic phenomena in the field of quantum physics, what is commonly known as quantum chaos. The results show a clear distinction of intensity patterns from the double-slit experiment depending on the shape of the resonator. Besides, the time decay probability in open billiards with regular and chaotic dynamics is extensively investigated.