Populations of widely distributed species encounter and must adapt to local environmental conditions. However, comprehensive characterization of the genetic basis of adaptation is demanding, requiring genome wide genotype data, multiple sampled populations, and an understanding of population structure and potential selection pressures. Here, we used SNP genotyping and data on numerous environmental variables to describe the genetic basis of local adaptation in 21 populations of teosinte, the wild ancestor of maize. We found complex hierarchical genetic structure created by altitude, dispersal events and admixture among subspecies that complicated identification of locally beneficial alleles. Patterns of linkage disequilibrium revealed four large inversion polymorphisms showing clinal patterns of frequency. Population differentiation and environmental correlations suggest that both inversions and intergenic polymorphisms are involved in local adaptation.