Many people, when talk of ancestry arises, say "I am Heinz 57 Variety", chiefly due to the melting pot called America. But, in reality, it is simpler than that--and at the same time more complex. Studying the world of DNA has changed my view of ancestry entirely. We inherit two sets of genes, one from each of our parents. These genes determine our appearance, intelligence, and other traits and we can certainly favor one parent over the other in regard to all that. We also inherit our blood type from one or the other of our parents. These genes or alleles are very useful when it comes to determining our recent relatives, if that is in doubt but, in a most basic sense, we are never "Heinz 57 Variety". That's because our "ancestral" DNA never varies, even though, living in a melting pot society, the various ethnic types that contributed to who we are certainly influenced other things about us.
If you are a male, you have inherited what is called y-DNA from your father in a chain that goes back indefinitely. This DNA can be broken down into a haplogroup and the haplogroup into sub-clades so that one can pretty well narrow down what part of the world your distant male ancestor came from. Studying the various surnames of men who have been tested by companies such as Family Tree DNA in various haplogroups and their subclades, it is quite amazing to see how these last names which seem to belong to various ethnicities--belong to persons who are related, regardless. That's right. Your last name can be Bailey but you can still have the same common ancestor as a man called Goldberg. There were times when certain areas of the globe, including the Middle East and Europe, were devastated by catastrophic diseases. On account of them many male lines died out and it was basically a case of the survival of the fittest. In other words, at these dreadful periods in history the progenitors, men who were able to perpetuate their y-DNA into the future, became relatively few. Minorities, like the Jews, were hit especially hard and that is why so many Jewish men with dozens of different last names [last names can be acquired by various means and are something relatively recent in the history of Mankind] have a common ancestor. Of course, persons who lived in distant lands like the Far East or were isolated by great bodies of water, such as the Americas or even Scandinavia usually do not fit into this picture because foreigners normally did not go there in antiquity. Some places were simply too far, too cold, beyond great mountains, or their men had reputations of being too fierce. But, sometimes, for certains reasons, men went far from their own lands--like the crusaders did to battle over Jerusalem.
Of course, if you are a male, you also inherited your mothers mitochondrial DNA--but you cannot pass that on to your children. You just pass your y-DNA on to your sons. Mitochondrial or mtDNA also has haplogroups and it is not at all rare for a man's mtDNA to come from a different part of the world than his y-DNA did. One of the reasons is that wandering men married or at least procreated with local women. Mitochondrial DNA is passed on from mother to daughter in an unbroken chain going back many thousands of years. If you are a female, the haplogroup your mtDNA belongs to is your unchanging ethnicity. This has nothing to do with religion, citizenship--or any group of which you might consider yourself a part. It is who you are in the most basic sense. You do not inherit y-DNA from your father if you are a female, just some of his genes. Being a woman, if you want to know where your remote paternal ancestors come from, your father or a brother, an uncle or a male cousin, need to be tested. Your own DNA is of no use for determining this.
The science of microbiology or DNA testing has shown that people have many more relatives everywhere than they ever imagined--and that people are more alike than they ever considered. DNA is immune to prejudice and national chauvanism. It does not lie. You may have believed your great-great-grandfather came from Ireland--and that may be so--but his own ancestors might have lived in Spain.