The field of nitric oxide (NOx) production combined with turbulent flow is a complex issue of combustion, especially for the different time scales of reactions and flow in numerical simulations. Around this, a series of approach methods, including the empirical formula approach, the computational fluid dynamics (CFD) approach coupling with an infinite rate chemical reaction, the chemical reaction networks (CRNs), and the CFD approach coupling with CRNs, were classified, and we discussed its advantages and applicability. The empirical-formula approach can provide an average range of NOx concentration, and this method can be involved only in special scenarios. However, its simplicity and feasibility still promote practical use, and it is still widely applied in engineering. Moreover, with the help of artificial intelligence, this method was improved in regard to its accuracy. The CFD approach could describe the flow field comprehensively. In compliance with considering NOx formation as finite-rate chemical reactions, the NOx concentration distribution via simulation cannot match well with experimental results due to the restriction caused by the simplification of the combustion reaction. Considering NOx formation as a finite-rate chemical reaction, the CRNs approach was involved in CFD simulation, and the CRNs approach could forecast the NOx concentration distribution in the flow field. This article mainly focuses on the simulation method of nitric oxide (NOx) production in different combustion conditions. This review could help readers understand the details of the NOx formation mechanism and NOx formation prediction approach.