This article seeks to help readers understand the MOVPE growth of nitride semiconductors as a part of science. MOVPE is the abbreviation for metalorganic vapor-phase epitaxy. Therefore, the precursors used are metalorganic gases and ammonia. The precursors decompose or react with others in the gas phase. The obtained reactive molecules form semiconductor layers on substrates. Those growth reaction pathways and the polymer formation will be discussed numerically for GaN, InN, InGaN, AlN, and AlGaN in this article. For those materials, the numerical analyses of growth rate and alloy composition exhibited the qualitative and quantitative agreements with experiments. The reader can see the growth mechanism, and experts will understand the current MOVPE conditions of nitride semiconductors.