The formation of terrestrial and gas giant planets has likely imprinted signatures on the chemical composition of their parent stars, as shown for example by the higher occurrence of giant planets for higher stellar metallicities. There are two new signatures that have been recently proposed by Meléndez et al. (2009, 2012) and Ramírez et al. (2009, 2010) for the formation of rocky planets, and by Ramírez et al. (2011) for gas giant planets. We review here our on-going work on the planet-star connection using solar twins, for which chemical abundances are being obtained at unprecedented precision (0.01 dex).