Association or linkage disequilibrium (LD)-based mapping strategies are receiving increased attention for the identification of quantitative trait loci (QTL) in plants as an alternative to more traditional, purely linkage-based approaches. An attractive property of association approaches is that they do not require specially designed crosses between inbred parents, but can be applied to collections of genotypes with arbitrary and often unknown relationships between the genotypes. A less obvious additional attractive property is that association approaches offer possibilities for QTL identification in crops with hard to model segregation patterns. The availability of candidate genes and targeted marker systems facilitates association approaches, as will appropriate methods of analysis. We propose an association mapping approach based on mixed models with attention to the incorporation of the relationships between genotypes, whether induced by pedigree, population substructure, or otherwise. Furthermore, we emphasize the need to pay attention to the environmental features of the data as well, i.e., adequate representation of the relations among multiple observations on the same genotypes. We illustrate our modeling approach using 25 years of Dutch national variety list data on late blight resistance in the genetically complex crop of potato. As markers, we used nucleotide binding-site markers, a specific type of marker that targets resistance or resistance-analog genes. To assess the consistency of QTL identified by our mixed-model approach, a second independent data set was analyzed. Two markers were identified that are potentially useful in selection for late blight resistance in potato.