The increasing promotion of a hydrogen-based economy and the use of low-carbon energy sources is critical to the global drive toward carbon neutrality by 2050, and ammonia is among the most promising intermediate products. The current industrial method for ammonia synthesis is the Haber-Bosch (H-B) process, which requires large amounts of fossil fuels, high temperatures and pressures, significant capital investment, and environmental issues. An alternative research interest focusing on plasma catalysis offers a clean, sustainable, and flexible alternative method to convert nitrogen into active species for ammonia (NH3) synthesis, but the science of ammonia synthesis using plasma technologies is still in its infancy. In the current review, we summarize the roles of catalyst materials and different plasma-excitation methods (i.e., dielectric barrier discharge (DBD), microwave (MW), gliding arc (GA), and radio-frequency (RF)) for plasma-based ammonia synthesis. We discuss the mechanisms of NH3 synthesis in the presence of a plasma with a catalyst under different plasma conditions. We summarize recent developments and the key challenges related to plasma catalytic NH3 synthesis, scaling-up possibilities, economic concepts, and an outlook for the future. Finally, this review aims to provide a detailed overview of the emerging ammonia synthesis technologies developed to effectively store green hydrogen for future applications.