Time-varying systems present unique opportunities for developing advanced electromagnetic and photonic devices. While research in this area originated more than fifty years ago, it is only in recent years that there has been a significant surge of research interest and momentum towards developing time-varying electromagnetic systems. This resurgence is driven partly by the realization that such systems may outperform traditional devices and overcome established performance limitations, such as the Bode–Fano limit, the delay-bandwidth limit, the Rozanov limit, and the Chu-Harrington limit. This dissertation demonstrates how recent advancements in this emerging field can be utilized to achieve unique phenomena and capabilities surpassing those of time-invariant systems. Furthermore, it is shown how the unique properties of the temporal dimension, particularly in terms of causality and energy conservation, introduce distinct challenges and physical limitations specific to time-varying systems, despite the often-invoked space-time duality in wave physics.