It has been recently shown that the chemical composition of the Sun is anomalous when compared to most nearby stars of very similar fundamental parameters, so-called solar twins. Compared to these stars, the Sun is deficient in refractory elements relative to volatiles, a finding that we speculate is a signature of the terrestrial planet formation that occurred around the Sun but not in the majority of solar twins. I will discuss these and newer related results, the strengths and weaknesses of our planet formation interpretation, as well as our plans for future observations that can help us better understand the nature of the abundance trends found.