Platinum group metals (PGMs) are a group of six metals with high market value and key importance to many industrial sectors. Due to their low prevalence in the Earth’s crust and high demand, these metals have been recognized as critical materials for many years. Along with economic development, the natural resources of the platinum group metals are gradually depleting, which is accompanied by the need to recover PGMs from secondary sources. The solutions resulting from the processing of such materials are characterized by high content of impurities and low content of precious metals. For this reason, in order to obtain pure metals, it is extremely important to choose an effective, selective method for the recovery and separation of the platinum group metals. This review focuses on the most important aspects of the characteristics of the PGMs, including their properties and occurrence, the processing of natural and secondary raw materials and the role of liquid–liquid extraction in the selective separation of metals from this group, not only on a laboratory scale but, above all, on an industrial scale. In addition, this study collects information on the most commonly used, commercially available extractants, based on current reports, taken from the scientific literature.