A summary of various high-frequency techniques is presented for analyzing the electromagnetic radiation from antennas in the presence of their host environment. These techniques provide physical insight into antenna radiation mechanisms and are found to be highly efficient and accurate for treating a variety of practical antenna configurations. Examples to which these techniques have been applied include open-ended waveguide antennas, horn and reflector antennas, and antennas on aircraft and spacecraft. The accuracy of these techniques is established via numerical results which are compared with those based on other independent methods or with measurements. These high frequency methods can be combined with other techniques, through a hybrid scheme, to solve an even greater class of problems than those which can be solved in an efficient and tractable manner by any one technique alone.>