Every living organism is composed of certain substances such as DNA, RNA, and proteins. Closely related organisms generally have a high degree of agreement in the molecular structure of these substances, while the molecules of organisms distantly related usually show a pattern of dissimilarity. Molecular phylogeny uses such data to build a "relationship tree" that shows the probable evolution of various organisms. Not until recent decades, however, has it been possible to isolate and identify these molecular structures. That it is now possible to do so can be seen by the ever more popular use of genetic testing to determine a child's paternity, as well as the emergence of a new branch of criminal forensics focused on genetic evidence.
The effect on traditional scientific classification schemes in the biological sciences has been dramatic as well. Work that was once immensely labor- and materials-intensive can now be done quickly and easily. As a result many branches of the phylogenetic tree have been disassembled and reassembled into patterns based on molecular identification rather than on the previous system of taxonomy based on morphology.
Because it is now possible to infer a gene's relationships by the existence of molecular similarities between it and other genes, it is also possible to use that information to determine the relationships of organisms based on the presence or absence, and the DNA sequence, of various genes.
An excellent summary of the state of the art can be found at Gary Olsens Molecular Phylogeny website: http://www.bact.wisc.edu/MicrotextBook/ClassAndPhylo/molPhylogeny.html