Gallium and indium are crucial metals in various industries, such as the medical and telecommunication industries. They can find applications as pure metals, alloys and alloy admixtures, oxides, organometallic compounds, and compounds with elements such as nitrogen or arsenic. Recovery of these two metals from waste is an important issue for two main reasons. First, gallium and indium are scattered in the Earth’s crust and their minerals are too rare to serve as a primary source. Second, e-waste contributes to the rapidly growing problem of Earth littering, as its amount increased significantly in recent years. Therefore, it is essential to develop and implement procedures that will enable the recovery of valuable elements from waste and limit the emission of harmful substances into the environment. This paper discusses technological operations and methods that are currently used or may be used to produce pure gallium and indium or their oxides from waste. The first step was described—waste pretreatment, including disassembly and sorting in several stages. Then, mechanical treatment as well as physical, chemical, and physicochemical separations were discussed. The greatest emphasis was placed on the hydrometallurgical methods of gallium and indium recovery, to be more precise on the extraction and various sorption methods following the leaching stage. Methods of obtaining pure metals or metal oxides and their refining processes were also mentioned.