The production of copper from sulfide minerals results in a significant amount of waste from the pyrometallurgical process, including slag, electrostatic precipitator (ESP) dust, anode slime, etc. Historically, this waste has been disposed of near the smelter plant. Currently, 2.2 tons of slag and ~50 kg/ton feed of ESP dust are generated per ton of blister copper and are granulated for more accessible transportation and disposal. Additionally, anode slime accounts for 0.2–0.8% of the refined copper production. However, it is essential to consider sustainability by recycling these wastes to reduce the environmental impact caused by processing copper sulfide concentrates. Various laboratory tests are conducted to concentrate and separate metals and materials to scale up to pilot and industrial levels. The results of pyrometallurgical and hydrometallurgical experiments demonstrate the technological advances for recovering critical metals. The importance of high-temperature oxidation of the slag to release metal values is evident from the reported endeavors. The present study provides an overview of the current processing for recovering critical metals from some copper extraction waste streams. It provides an account to analyze the sustainability and can catalyze the impact of critical metal recovery by recycling the waste materials.