Synchronization is a most striking phenomenon in ensembles of coupled oscillators. In this talk I will discuss basic mathematical models used in the field and the approaches to their analysis. Furthermore, inverse problems of inferring the coupling structure from the observations of oscillatory dynamics will be discussed. The presentation is partially based on the recent review [A Pikovsky and M Rosenblum, "Dynamics of globally coupled oscillators: Progress and perspectives", CHAOS 25, 097616 (2015)].