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 NO_x 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.