With the urgent demand for global carbon neutrality, ammonia is increasingly seen as a promising alternative to traditional fossil fuels for use in internal combustion engines (ICEs) and gas turbines (GTs). However, the practical industrial applications have faced obstacles due to certain unfavorable combustion characteristics of ammonia. This necessitates the development of advanced and innovative computational tools to enable the clean and efficient utilization of ammonia fuels. The combination of lower cost, enhanced controllability, and detailed information on local and global fluid flow, heat transfer, and mass transfer phenomena provided by Computational Fluid Dynamics (CFD) simulations makes it indispensable for the development and optimization of ammonia-fueled ICEs and GTs, paving the way for cleaner and more efficient propulsion systems within the energy sector. Herein, this work systematically introduces and analyzes ammonia-fueled ICEs and GTs along with their numerical simulation methods, models, and chemical kinetic mechanisms. The similarities and differences of various simulation methods in ammonia fuel-related combustion are summarized, highlighting those methodologies applied in the numerical studies under the corresponding conditions, and focusing on the current state, and shortcomings of utilzing CFD in ICEs and GTs. By providing this comprehensive information, options and references are provided for related numerical simulation research. Finally, based on the results of the current simulation studies, future goals are indicated for advancing CFD simulation of ammonia-fueled ICEs and GTs, which will contribute to the low-carbon transition of industry.