Abstract: This talk will explain some result on the intersection cohomology of the moduli space of semistable logarithmic G-Higgs bundles on a smooth curve, where G is a reductive group. For any given degree d in the algebraic fundamental group of G, I will report on a new uniform description of the decomposition theorem for the corresponding Hitchin fibration of degree d logarithmic G-Higgs bundles. I will also discuss consequences to cohomological degree independence in this setting. This is based on joint work with Mark Andrea de Cataldo, Roberto Fringuelli and Mirko Mauri.