Sustainable mobility is a legal and public demand. An important measure to clean the exhaust gas of diesel engines is the conversion of nitric oxides with selective catalytic reduction (SCR). The development of SCR systems can be strongly supported by numerical methods. This review article is to document the status of the CFD-simulation method with respect to the preparation of the injected urea-water solution, the turbulent transport of ammonia and the assessment of solid deposits coming from liquid film. Comparisons with measurements for realistic sprays and mixing sections are given.