After a brief review of the use of genetic markers for describing human population relationships , I will review our study of the genetic fine structure of the population of the British Isles. This is based on a rural sample of more than 2000 volunteers from throughout the UK each of whose four grandparents came from more or less the same area and using a method of analysis on data on about 500,000 SNPs called fineSTRUCTURE, that takes into account linkage disequilibrium. The results show a remarkable concordance between genetic and geographical clustering. This clustering can be interpreted in terms of genetic admixture from the European countries that surround the UK and related to the known history and archaeology of the British people. Some preliminary results of our studies on the genetics of facial features of this British population sample will also be outlined.