This paper summarizes the research activities conducted at the University of Siena during the past 10 years on the truncated Floquet wave diffraction theory under the continuous guidance of Professor Felsen who recently passed away. This paper analyzed and validated the diffraction phenomena in both the frequency and time domains pertaining to large planar phased arrays of different topologies and environments and with quite general excitation profiles. The themes chosen here are the ones dearest to Professor Felsen.