The literature on horn antennas dedicated to radio astronomy and satellite communications applications is very extensive and at times disjointed, relevant contributions being distributed as far back as from the 60's until the present today. This work combines a compact but complete review of the different theories, methodologies and techniques used to describe corrugations and metamaterials in their application to feedhorns used in radio astronomy and satellite communications along with some new work to help explain the theory in a more practical way. Starting with the hybrid-mode condition firstly corrugated horns are explained describing soft and hard boundaries and also the theory from a plasmonic optics point of view. Following this the use of metamaterials in order to design horn antennas with quasi-null cross-polarization and low E-Plane sidelobes level over an ultra-wideband is described. The objective of this work is to help to ease the learning curve of the post graduate students and young professionals dedicated to these tasks, and try to inspire the work of the senior professionals toward a new direction and approach.