The need to drive towards sustainable metal resource recovery from end-of-cycle products cannot be overstated. This review attempts to investigate progress in the development of recycling strategies for the recovery of strategic metals, such as precious metals and base metals, from catalytic converters, e-waste, and batteries. Several methods for the recovery of metal resources have been explored for these waste streams, such as pyrometallurgy, hydrometallurgy, and biohydrometallurgy. The results are discussed, and the efficiency of the processes and the chemistry involved are detailed. The conversion of metal waste to high-value nanomaterials is also presented. Process flow diagrams are also presented, where possible, to represent simplified process steps. Despite concerns about environmental effects from processing the metal waste streams, the gains for driving towards a circular economy of these waste streams are enormous. Therefore, the development of greener processes is recommended. In addition, countries need to manage their metal waste streams appropriately and ensure that this becomes part of the formal economic activity and, therefore, becomes regulated.