The rigorous mathematical analysis of quantum many-particle systems has a long history, dating back to the early days of quantum mechanics. In case of (dilute) Bose gases, there has been a period of renewed interest since the first experimental observation of Bose–Einstein condensation in trapped alkali gases in 1995 (Nobel price in 2001). In the first part of the talk I will present two key results concerning the Bose gas at zero temperature that have been very influential in the last 20 years. Afterwards, I will describe how my collaborators and me substantially extended the relevant techniques to provide the first proof of the Bose-Einstein condensation phase transition for two realistic continuum models. In the last part of the talk I will report on a recent result concerning the derivation of effective evolution equations for Bose gases initially prepared in approximate Gibbs states.