Surreal numbers strike by the richness of their structure together with their universality: generalization of the reals and of the ordinal numbers, representation as generalized series with real coefficients, universal domain for real closed exponential fields. Several other important achievements have been obtained recently: structure of real differential field of transseries (Berarducci-Mantova), universal domain for Hardy fields (Aschenbrenner-van den Dries-van der Hoeven). Even a notion of partial composition has just been developed (Berarducci-Mantova). In this talk, we'll get started with an accessible presentation of surreal numbers (definitions and classical results). Then, we'll develop some aspects of the cited recent works. If time permits, we'll mention a work in progress with Berarducci, S. Kuhlmann and Mantova.