Recycling valuable and essential materials from end-of-life devices and waste is becoming an obligation for all of us, considering the well-being of organisms (including the level of our actual living standards) and preservation of Earth resources. Palladium is one of the most important platinum-group metals, with several determinant technological applications; therefore, investigation on its sustainable recovery by hydrometallurgical methodologies, from secondary resources, has been intensive in recent years. This paper summarizes the major achievements of the author’s research group to cope with this goal, through the development of novel solvent extraction (SX) systems aiming to efficiently and selectively recover Pd(II) from aqueous leaching solutions coming from the treatment of spent automotive and petrochemical catalysts. The clear advantages of using sulfur-containing diamides as Pd(II) extractants are highlighted, reflected by: (1) the quantitative Pd(II) extraction from aqueous solutions up to 6 mol L−1 HCl; (2) the excellent extractant/Pd(II) molar ratios at saturation; (3) the reutilization profile upon a limited set of successive extraction-stripping cycles; (4) their selectivity for Pd(II) extraction over Pt(IV), cerium and aluminum. The data obtained is critically compared with those achieved with a commercial phosphine sulfide derivative, tested under similar experimental conditions. The most relevant drawback is the progressive accumulation of aluminum upon the repeated SX utilization of the organic solvents, whose contamination proves to be very difficult to remove.