The year 1995 saw the discoveries of both Gliese 229B, the first unambiguously detected brown dwarf, and 51 Peg b, the first gas giant orbiting a sunlike star. Since then discoveries of both types of objects have proliferated, with 1070 extrasolar planets and 1281 brown dwarfs verified as of January 17, 2014. The new discoveries led to a parallel renaissance in theoretical investigations of planets and low-mass stars. Yet almost 20 years after the first giant planet discoveries, even a question as basic as whether giant planets grow bottom-up from colliding dust grains or top-down from collapsing gas does not have a simple answer. The diversity seen in both Solar System objects and extrasolar planets/brown dwarfs points to at least three different formation pathways for gaseous spheres. Furthermore, the chemical origins of our own Solar System are still uncertain as planetary scientists try to figure out what lies under the surface of each world. For example, Jupiter and Saturn have solid cores that are several times the mass of Earth, made up of at least 30% ice. Giant planets require massive solid cores to provide the gravitational force required to build large atmospheres. However, planet formation models using cores of rock and HO ice alone cannot explain the rapid formation of Saturn, Uranus or Neptune. New simulations show that volatile molecules besides HO such as methane, hydrocarbons and cyanides, may be incorporated into the cores of the outer planets. These frozen volatiles may provide the missing mass necessary to build the atmosphere of Saturn. To understand the growth and development of planets, one must practice planetary archaeology. It is possible to read the fossil record of planet formation by measuring properties such as star chemical composition, planet density and type of orbit. Dodson-Robinson's group uses analytical theory and numerical simulations of the dynamical and chemical environment of planet growth to uncover the formation histories of as many worlds as possible. We also use spectroscopy to chemically analyze stars with planets and orbiting dust.