This thesis aims at revealing the fundamental guiding and coupling properties of nonreciprocal electromagnetic surface waves on magneto-optical or gyromagnetic media and designing novel applications based on the properties. We introduce the background in the first chapter. We then describe the concept of nonreciprocity and the main calculation method in the second chapter. In the third chapter, we show that one-way waves can be sustained at the edge of a gyromagnetic photonic crystal slab under an external magnetic field. We also investigate the coupling between two parallel one-way waveguides. We reveal the condition for effective co-directional and contra-directional coupling. We also notice that the contra-directional coupling is related to the concept of a “trapped rainbow”. In the fourth chapter, we address the concept of a “trapped rainbow”. It aims at trapping different frequency components of the electromagnetic wave packet at different positions in space permanently. In previous structures, the entire incident wave is reflected due to the strong contra-directional coupling between forward and backward modes. To overcome this difficulty, we show that utilizing nonreciprocal waveguides under a tapered external magnetic field can achieve a truly “trapped rainbow” effect at microwave frequencies. We observe hot spots and relatively long duration times around critical positions through simulations and find that such a trapping effect is robust against disorders. Lastly, in the fifth chapter, we study the one-way waves in a surface magnetoplasmon cavity. We find that the external magnetic field can separate the clockwise and anti-clockwise cavity modes into two totally different frequency ranges. This offers us more choices, both in the frequency ranges and in the one-way directions, for realizing one-way components. We also show the waveguide-cavity coupling by designing a circulator, which establishes the foundation for potential applications. / <p>QC 20160816</p><p></p>