There is a deep connection between star formation and AGN activity, at all redshifts, which profoundly impacts the mass assembly history of galaxies. The nature of the connection however remains controversial, due to, for example, evolution in the AGN and starburst duty cycles, and the obscuring effect of dust. The luminous type 1 quasars are an insightful population to study in this context; accretion rates can be estimated from the UV/optical continuum shape, black hole masses can be estimated from rest-frame UV line properties, and star formation rates can be cleanly estimated from far-infrared imaging from Herschel. Our group has been studying the relationships between star formation, black hole masses and accretion rates in luminous type 1 quasars over 0.5<z<3, using data from Herschel and the SDSS. In this talk I will present some of our latest results, and discuss some implications from them for galaxy assembly at z>1.