New measurements of jet quenching observables in heavy-ion collisions at RHIC and at the LHC demand an increased precision in the theory calculations describing medium-induced radiation of gluons. Closed expressions for the gluon spectrum including the full resummation of multiple scatterings have been known for the past 20 years. However, until very recently, they were only evaluated under restrictive approximations. I will present here a new method allowing the evaluation of this spectrum without any further approximations for static media. I will also revisit the conceptual and computational issues arising when embedding this (or any other approach including multiple scatterings) into dynamically evolving plasmas. I will show several paths to overcome these difficulties and present results on the fully-resumed spectrum for longitudinally evolving media.