This paper reviews current knowledge about genes for resistance to Septoria tritici blotch (STB) of wheat, caused by Zymoseptoria tritici (formerly Mycosphaerella graminicola). These genes can be placed into two classes, although a few may have characteristics of both classes. Qualitative resistance is controlled by genes which control large fractions of genetic variation, 21 of which have been discovered and mapped so far. Most of them have been shown to be genotype-specific, being effective against the minority of Z. tritici isolates which are avirulent, and Stb6 has been shown to control a gene-for-gene relationship. Most qualitative resistances are unlikely to be durable and some formerly effective genes have been overcome by the evolution of pathogen virulence. Quantitative resistance is generally controlled by genes with small-to-moderate effects on STB. They have generally weaker specificity than qualitative genes and have provided more durable resistance. 89 genome regions carrying quantitative trait loci (QTL) or meta-QTL have been identified to date. Some QTL have been mapped at or near loci of qualitative genes, especially Stb6, which is present in several sources of resistance. Another gene of particular interest is Stb16q, which has been effective against all Z. tritici isolates tested so far. In addition to resistance, the susceptibility of wheat cultivars to STB can also be reduced by disease escape traits, some of which may be undesirable in breeding. The fundamental requirements for breeding for STB-resistance are genetic diversity for resistance in wheat germplasm and a field trial site at which STB epidemics occur regularly and effective selection can be conducted for resistance combined with other desirable traits. If these are in place, knowledge of resistance genes can be applied to improving control of STB.