Classic phylogenetics dealt mainly with physical, or morphological features - size, color, number of legs, etc. Modern phylogeny uses information extracted from genetic material - mainly DNA and protein sequences. The characters used are usually the DNA or protein sites (a site means a single position in the sequence) after aligning several such sequences, and using only blocks which were conserved in all the examined species.
An interesting example is a research project that used phylogenetics in order to trace the origins of the human population on earth. Researchers investigated the mitochondrial DNA of 182 people all over earth (the mitochondrial DNA is especially good for phylogenetic research since it is copied completely from mother to son, without recombining with the father's DNA). The phylogenetic analysis provided evidence that all humans have a common female ancestor who lived in Africa ("African Eve").
When studying phylogeny using nuclear genes, we encounter a serious problem. During evolution, it is very common for a gene to be duplicated. The copies continue to evolve separately, resulting in two (or more) similar instances of the same gene along the genome of a species. Therefore, when discussing matching genes in different species, we differentiate between orthologous matches - which means both genes are ``the same'' gene in the strong sense - they are connected directly, and not through a duplication, paralogous matches - which are the result of some duplication along the evolutionary line, and xenologs (horizontal transfers) which are genes that are transfered between organisms in other ways (e.g., by virus). Therefore, if we base our analysis on paralogs or xenologs (rather than orthologs) we are in big trouble. However, throughout this lecture we will assume there were no gene duplications.
Note: In this lecture we shall refer to the objects whose phylogeny is in question as species. However, the discussion is valid not only to the phylogeny of different species, but also to other objects, e.g., duplicated genes of the same species. We shall also often refer to characters as sites, because this is the most common case.