F1 hybrids in a number of crop species are able to out-perform the inbred varieties. To exploit hybridity in wheat, difficulties associated with the F1 grain production which mainly arise from wheat’s strong cleistogamous nature have to be addressed. For F1 wheat seed production, the female parent should be male-sterilized, have open florets and receptive stigma to access incoming pollen; meanwhile, the male parent should show high anther extrusion (AE) to shed pollens outside the floret for increased cross pollination. The results in this thesis show that AE is a diverse and heritable trait. The association mapping of AE shows that it is under the control of a number of genetic loci, some of which act favorably and others unfavorably. Intra-chromosomal linkage-disequilibrium (LD) estimation to demarcate the QTL regions helps to study the function and expression of the QTL genes. As association analyses revealed a highly complex nature of AE, a breeding strategy based on genomic selection can be applied. The results of genomic prediction revealed high prediction accuracy for AE. Understanding the genetic basis of AE will help to exploit heterosis in wheat.