The ever-growing demand for low power, high performance, cost-effective, low-profile, and highly integrated wireless systems for emerging applications has triggered the need for the enormous innovations in wireless transceiver systems, components, architectures and technologies. This is especially valid for the antenna which is an integral component of the wireless transceiver systems and contributes significantly in determining their overall performance. Antenna-on-Chip (AoC) is an alternative antenna technology, which has drawn a substantial attention in recent days because of its various benefits over off-chip antenna technology. A few of these benefits include miniaturization, low power, low cost, and high integration of the wireless modules. Motivated by these valuable advantages and to unveil the true potential of the AoCs, this article presents, for the first time, a comprehensive survey of the suitability, advantages, and challenges of the AoCs for the emerging wireless applications such as 5th generation (5G) Wireless Systems, Internet-of-Things (IoT) Wireless Devices and Systems, Wireless Sensor Networks (WSNs), Wireless Interconnects, Wireless Energy Transfer, Radio Frequency (RF) Energy Harvesting, Biomedical Implants, Unmanned Aerial Vehicles (UAVs), Autonomous vehicles, Innovative characterization methods for Integrated Circuits (ICs) and Antennas, and Smart City. In addition, this article presents the current stateof-the-art of the AoC's applications by classifying their applications in Millimeter-Wave (MM-Wave) band, Terahertz (THz) band, and low-frequency bands. The article also investigates and describes some useful methods for the mitigation of the challenges and issues posed by the emerging applications for the realization of the AoCs in a systematic manner. A concise description of the future directions of the AoCs with respect to each emerging application is also a part of this article. It is expected that this well-structured and organized survey will not only act as an excellent source of scholarship for the relevant research community, but also open up a world of novel research opportunities.