There have been significant developments in the field of numerical methods for diffraction problems in recent years, and as a result, it is now possible to perform computations with more than ten million unknowns. However, the importance of asymptotic methods should not be overlooked. Not only do they provide considerable physical insight into diffraction mechanisms, and can therefore aid the design of electromagnetic devices such as radar targets and antennas, some objects are still too large in terms of wavelengths to fall in the realm of numerical methods. Furthermore, very low Radar Cross Section objects are often difficult to compute using multiple methods. Finally, objects that are very large in terms of wavelength, but with complicated details, are still a challenge both for asymptotic and numerical methods. The best, but now widely explored, solution for these problems is to combine various methods in so called hybrid methods. Asymptotic and Hybrid Methods in Electromagnetics is based on a short course, and presents recent developments in the field.