Recently, the analysis of a descendant's DNA can be used to establish or resolve ancestry relationships and geographic origins. At this time no DNA information is available for any of our descendants.
There are generally three kinds of DNA analysis with very different information about ancestry, Y-chromosome analysis, mitochondrial analysis, and general chromosome analysis (autosomal). The X-chromosome can also be analyzed but is harder to use.
Human chromosomes in each cell come in pairs of DNA strings. There are 22 general chromosome pairs plus one sex chromosome pair. One chromosome in each pair comes from the father and the other from the mother, so the child is the result of their overlapping characteristics. The sex chromosome pair is YX for a male and XX for a female. During creation of the egg and sperm cells, meiosis may mix/recombine the two strings of an individual's pair while making the single string in the egg or sperm. The single strings from the egg and sperm pair-up during fertilization. The successful sperm contains either an X or a Y chromosome and hence determines the sex of the child.
The Y-chromosome causes the fertilized egg to develop into a male. Since it can only come from the father's sperm, any change/mutation over time passes only from male to male to male. The Y-chromosome, especially the sex gene, is stable over time but changes in other parts of the Y-chromosome DNA can be used to trace the all-male-line ancestry by comparison to other, known descendants.
Mitochondria are bacteria-like organelles in each cell that produce energy. Their short, circular, DNA string controls their function. Because mitochondria exist only in the egg, they are passed only from the mother and hence any change/mutation over time passes only from female to female to female. So the mitochondrial DNA differences can trace the all-female ancestral line by comparison to other, known descendants.
The X-chromosome occurs in both males and females. It can come from the paternal grandmother unmixed in the sperm for females or the maternal grandfather-grandmother mixed string in the egg for both males and females. No part comes from the paternal grandfather because the father got only a Y-chromosome from him. This makes the inheritance pattern goring back in time more complex, so this test is just coming into use in genealogy.
The other 22 chromosome pairs (autosomal) are mixed at each meiosis and conception, and are pretty much useless for identifying specific lines. However, specific DNA differences can be compared with databases of other, individual DNA, and the patterns indicate the geographic origin of the ancestors as a group, or even find probable relations. For example, a person's ancestors may be 10% Scandinavian, 30 % Finnish, and 60% Western European. The more siblings and relatives analyzed, the more accurate this geographic pictures becomes, because each person inherits different parts of the parent's and grandparent's DNA.