It's obvious that maple species are more closely related to each other than they are to oaks, and that oaks and maples are more closely related to each other than to pines and spruces. These trees all share an older common ancestry as seed plants, and a more ancient relationship as vascular plants. On a larger scale the green plants all share characteristics such as chlorophylls and cellulosic cell walls that do not occur in animals or fungi. All of us multicellular organisms (and many that are single-celled) are eukaryotes - each of our cells contains a nucleus where our chromosomes are housed. This suggests a long evolutionary history, and the fossil record provides additional corroborating evidence.

We assume (unless there is evidence to suggest otherwise) that these shared characters are truly shared, that they are homologous, that they appeared only once and have been carried along with the diverging lineages of evolution. Function is less important - the wings of birds and insects are analogs, but they evolved independently and are not homologs. There is evidence that very simple life forms arose more than once, and this implies that life is the result of natural laws.

Systematists make branching diagrams that look something like family trees. Early naturalists, such as Linnaeus, tried to generate natural groupings of organisms to reflect God's creation, the "great chain of being." Once Darwin's theory caught on and we began to understand a little about genetics, systematics was approached in an evolutionary context. Evolutionary systematics tried to tie assumptions about adaptation and natural selection to hypothetical relationships among species. Evolutionary systematists were very knowledgeable, but their approach often contained too much opinion and too little evidence. With the rise of computers in the 1970s, numerical taxonomy or phenetics became popular. Numerical taxonomists preferred hard data to expertise, but they weren't selective and grouped species based on overall similarities.

In the 1950s, German biologist Willi Hennig developed a method called phylogenetic systematics or cladistics. Cladists group species based entirely on nested sets of shared characters, but not all characters are relevant. Characters exclusive to a single species (autapomorphies) are rejected because they offer no information about relationships among species. Synapomorphies are characters uniquely shared by two or more species, and serve to define a group (all mammals and only mammals have hair). A plesiomorphy is also a shared character, but it offers no new information about the group being studied (called the ingroup). Mammals are vertebrates, but so are other animals that are not mammals, so having a backbone tells us nothing new about mammals. However, if we are looking at all the animals on Earth, the possession of a backbone becomes a synapomorphy for a subgroup of all animals, the vertebrates.