We review briefly the recent progress in the determination of accurate and reliable electron affinities (EAs) of complex heavy systems with the view of assessing the reliability of the existing measured and/or calculated EAs of these systems. We demonstrate using slow electron collisions with complex heavy systems a novel and robust approach to the determination of reliable EAs from negative ion formation. From the Regge-pole calculated elastic total cross sections (TCSs), characterized by Ramsauer-Townsend (R-T) minima, shape resonances and dramatically sharp resonances manifesting anionic formation, we extract the anionic binding energies (BEs) for the ground, metastable and excited anionic states formed during the collisions. The ground state anionic BEs located at the absolute values of the R-T minima are identified with the systems’ EAs. Results for various complex heavy systems, including fullerene molecules are compared with available measurements and calculations.