Ammonia is a technically feasible carbon-free alternative fuel for industrial heat, power generation, and transport. The main advantages of using ammonia as a fuel are its low storage and transportation costs, low fire hazard and the availability of existing infrastructure. The present review addresses the following issues: combustion of ammonia and its mixtures in porous media, mechanisms of pyrolysis and oxidation of ammonia and safety of transportation and storage of ammonia and its mixtures. It has been shown that the combustion characteristics of ammonia and its mixtures in porous burners are promising in comparison to those in conventional burners. Significant effects of combustion in porous media include: an increase in temperature and combustion velocity, an expansion of flammability limits, and improvement in flame stability and power density. The current computational models for porous media combustion make it possible to qualitatively describe the characteristics of the process. Moreover, the quantitative results generally disagree with the experimental data. It can be concluded that modeling the combustion of mixtures with ammonia in porous burners remains a major challenge and further development of chemical mechanisms is necessary. The prospect of a global increase in the use of ammonia as a fuel will clearly require the development of new additional safety regulations in these industries.