The goal of systematics is to have the classification of biodiversity reflect its evolutionary history.
If this is done well two things will occur:
The phylogenetic trees we see will accurately represent evolutionary relationships between species.
The way organisms are classified will accurately represent how closely they are truly related.
What Allows Us To Trace Phylogeny?
Fossil Record: preserved remains and traces of what were once living organisms provide a wealth of information.
This is raw evidence of the relatedness of organisms.
Radiometric Dating: using our understanding of the radioactive decay of certain elements, we are able to determine the age of certain rocks and therefore place fossils in an accurate timeline.
Molecular Data: using a variety of techniques looking at DNA, RNA, and proteins, scientists have been able to show relatedness of organisms and determine their evolutionary histories.
It is becoming clear that these may be driving forces of evolutionary change, due to the rapid changes in the environment that they cause.
The major breakthrough in this area of research was the discovery of the impact crater in the Yucatán Peninsula that led to the demise of the dinosaurs 65 million years ago.