Originally, Bogoliubov theory has been developed in theoretical physics to study the properties of dilute Bose gases at low temperatures. In recent years, extensive work has been done on formalizing the theory into a rigorous framework. In this talk, I am going to discuss both Bogoliubov’s original ideas and recent progress in the formalization of this theory. In particular, I am going to focus on Bose gases in the so-called Gross—Pitaevskii regime, where N particles trapped in the unit torus interact through a potential with scattering length of the order 1/N. Moreover, I am going to present a recent extension of this approach to particles with relativistic dispersion.