Time-modulated arrays utilize time as an alternative beamforming method to augment existing analog/digital/hybrid wireless beamformers. The introduction of the time dimension in such dynamic antenna arrays may offer advantageous beamforming capabilities to emerging integrated sensing and communication (ISAC) applications, dramatically reducing the hardware complexity of their implementations. This paper reviews the state-of-the-art time-modulated arrays, with an emphasis on those reported in integrated-circuit (IC) technologies, such as complementary metal-oxide-semiconductor (CMOS), for wireless applications. Starting with an analytical framework of time-modulated arrays, their operation and beamforming characteristics are analyzed for multiple periodic switching schemes, including the ON/OFF amplitude-modulation scheme, the continuously-ON 0°/180° phase-modulation scheme, and the double switching scheme with even/odd-symmetry. Then, a survey of the main IC applications in which time-modulated arrays have been proposed is presented, including their ISAC applications in transmitter concurrent multi-beam generation, reflective relays that support multi-beam reception and transmission, spatio-temporal filtering that can be used for sensing, and receiver MIMO using one-wire interface and enhancing physical layer security in wireless communication. Afterwards, the performance characteristics of time-modulated arrays for both receiving and transmitting beamforming arrays are analyzed and compared with standard single-beam and multi-beam phased arrays. Finally, the potential challenges of time-modulated arrays, including the fixed-angle nature of their beams and the generated harmonics impact especially for transmitter arrays, are discussed.