In this talk I will first briefly review the status of our theoretical understanding of 4-lepton processes at the LHC, with a particular emphasis to their role in Higgs analysis.
Currently, such analysis somewhat suffer from the lack of precise enough predictions for SM background processes.
I will then describe the challenges that such computations pose and discuss powerful new theoretical ideas which allow to cope with them, focusing on their application to the calculation of two-loop gg -> 4l amplitudes.