The citation for Manjul Bhargava's recent Fields Medal mentions his improvement of my proof (partly with Will Schneeberger) of the 15- theorem, and his proof (with John Hanke) of the 290-theorem. I shall talk about the history of universal quadratic forms, which was started in 1770 by Lagrange's four squares theorem, and culminated about 20 years ago in these two theorems. I'll also talk about some related problems, some of which are still open.