Solid oxide fuel cells with protonic ion conducting electrolytes (H-SOFCs) are recognized and anticipated as eco-friendly electrochemical devices fueled with several kinds of fuels. One distinct feature of SOFCs that makes them different from others is fuel flexibility. Ammonia is a colorless gas with a compound of nitrogen and hydrogen with a distinct strong smell at room temperature. It is easily dissolved in water and is a great absorbent. Ammonia plays a vital role as a caustic for its alkaline characteristics. Nowadays, ammonia is being used as a hydrogen carrier because it has carbon-free molecules and prosperous physical properties with transportation characteristics, distribution options, and storage capacity. Using ammonia as a fuel in H-SOFCs has the advantage of its ammonia cracking attributes and quality of being easily separated from generated steam. Moreover, toxic NOx gases are not formed in the anode while using ammonia as fuel in H-SOFCs. Recently, various numerical studies have been performed to comprehend the electrochemical and physical phenomena of H-SOFCs in order to develop a feasible and optimized design under different operating conditions rather than doing costlier experimentation. The aim of this concisely reviewed article is to present the current status of ammonia-fueled H-SOFC numerical modeling and the application of numerical modeling in ammonia-fueled H-SOFC geometrical shape optimization, which is still more desirable than traditional SOFCs.