Time and frequency modulated arrays have numerous application areas including radar, navigation, and communications. Specifically, a time modulated array can create a beampattern with low sidelobes via connecting and disconnecting the antenna elements from the feed network, while the frequency modulated frequency diverse array produces a range-dependent pattern. In this paper, we aim to introduce these advanced arrays to the signal processing community so that more investigations in terms of theory, methods, and applications, can be facilitated. The research progress of time/frequency modulated array studies is reviewed and the most recent advances are discussed. Moreover, potential applications in radar and communications are presented, along with their technical challenges, especially in signal processing aspects.