Antennas on-chip are a particular type of radiating elements valued for their small footprint. They are most commonly integrated in circuit boards to electromagnetically interface free space, which is necessary for wireless communications. Antennas on-chip radiate and receive electromagnetic (EM) energy as any conventional antennas, but what distinguishes them is their miniaturized size. This means they can be integrated inside electronic devices. Although on-chip antennas have a limited range, they are suitable for cell phones, tablet computers, headsets, global positioning system (GPS) devices, and WiFi and WLAN routers. Typically, on-chip antennas are handicapped by narrow bandwidth (less than 10%) and low radiation efficiency. This survey provides an overview of recent techniques and technologies investigated in the literature, to implement high performance on-chip antennas for millimeter-waves (mmWave) and terahertz (THz) integrated-circuit (IC) applications. The technologies discussed here include metamaterial (MTM), metasurface (MTS), and substrate integrated waveguides (SIW). The antenna designs described here are implemented on various substrate layers such as Silicon, Graphene, Polyimide, and GaAs to facilitate integration on ICs. Some of the antennas described here employ innovative excitation mechanisms, for example comprising open-circuited microstrip-line that is electromagnetically coupled to radiating elements through narrow dielectric slots. This excitation mechanism is shown to suppress surface wave propagation and reduce substrate loss. Other techniques described like SIW are shown to significantly attenuate surface waves and minimise loss. Radiation elements based on the MTM and MTS inspired technologies are shown to extend the effective aperture of the antenna without compromising the antenna's form factor. Moreover, the on-chip antennas designed using the above technologies exhibit significantly improved impedance match, bandwidth, gain and radiation efficiency compared to previously used technologies. These features make such antennas a prime candidate for mmWave and THz on-chip integration. This review provides a thorough reference source for specialist antenna designers.