Abstract: I will present rigorous results on the effective properties of many-body systems consisting of multiple bosonic species. This will be based on joint works with A. Michelangeli and P.T. Nam. Concerning stationary properties, we were able to prove that, both in the mean field and Gross-Pitaevskii regime, the leading order of the ground state energy is captured by the minimum of a suitable effective functional. Moreover, in the ground state, all species of the mixture exhibit condensation. For mixtures in the mean field regime, we are also able to justify Bogoliubov theory, hence computing the next-to-leading correction to the ground state energy, and proving a norm approximation for the ground state. The above properties justify crucial assumptions for the theorems on the dynamical evolution that I will present. These are results of persistence of condensation for mixtures, which I will state and discuss both in the mean-eld and Gross-Pitaevskii regime.