Small satellites have revolutionized the space industry because of their variety of benefits over large satellites. Antennas are one of the key components of the small satellites, whose performance is very crucial for the overall performance of the satellite-based wireless systems. The stringent requirements of modern small satellites, such as the small size and mass, low-power, low-loss, and low-cost dictate the need for the alternative antenna technologies, as the traditionally employed off-chip antenna technology faces a number of severe constraints to meet this set of requirements. On-chip-antennas (OCAs) are one of such promising choices, which are more favorable than off-chip antennas in this respect. This article, therefore, presents a comprehensive survey of OCA capabilities for modern small satellite (micro-satellite, mini-satellite, nano-satellite, pico-satellite, femto-satellite, cubsat) applications for the first time. A number of key challenges posed by OCAs for small satellite applications are investigated and discussed analytically. The article also delineates a few future perspectives in this regard. This article will not only highlight a number of novel research opportunities for the relevant researchers but also urge them to propose innovative solutions for OCA design challenges for these applications.