Selection is a basic principle of evolution. Many approaches and studies have identified DNA mutations rapidly selected to high frequencies, which leave pronounced signatures on the surrounding sequence (selective sweeps). However, for many important complex, quantitative traits, selection does not leave these intense signatures. Instead, hundreds or thousands of loci experience small changes in allele frequencies, a process called polygenic selection. We know that directional selection and local adaptation are actively changing genomes; however we have been unable to identify the genomic loci responding to this polygenic, complex selection. Here we show that the use of novel dependent variables in linear mixed models (which allow us to account for population structure, relatedness, inbreeding) identify complex, polygenic selection and local adaptation. Thousands of loci are responding to artificial directional selection and hundreds of loci have evidence of local adaptation. While advanced reproduction and genomic technologies are increasing the rate of directional selection, local adaptation is being lost. In a changing climate, the loss of local adaptation may be especially problematic. These selection mapping approaches can be used in evolutionary, model, and agriculture contexts.