Advances in computing power, numerical algorithms and physical models have occurred at a remarkable pace during the past 40 years. Computations of multidimensional reacting flows are now performed routinely, and computational fluid dynamic (CFD)‐based tools are increasingly used in industry to test and design new combustors. Consequently, numerical combustion has become a diversified field with virtually unlimited literature, which makes it impossible to cover this topic in a single chapter. Therefore, the present discussion is limited to numerical simulations of reacting systems involving zero‐, one‐, and two‐dimensional combustion phenomena. Starting with the generalized form of the conservation equations and a general methodology for the computation of 3‐D reacting flows, several examples of simplified combustion systems are presented. These include flammability limits, flame blowout, transient ignition, 1‐D premixed flames, opposed‐jet flames, and transient 1‐D reacting systems, such as droplet ignition and combustion. Computations of 2‐D steady and unsteady flames using a DNS‐based code are also discussed. Examples here include the stability and emission characteristics of burner‐stabilized flames, and flame liftoff and blowout. Topics not covered include the modeling and computations of turbulent flames and multiphase reacting flows, including spray and coal combustion. In spite of its phenomenal growth, the field of numerical combustion continues to evolve, as exemplified by advances in high‐performance computing, modeling of turbulence–chemistry interactions, numerical flame diagnostics, and algorithms for the automatic generation of reaction mechanisms.