Synthetic dyes or colorants are key chemicals for various industries producing textiles, food, cosmetics, pharmaceutics, printer inks, leather, and plastics. Nowadays, the textile industry is the major consumer of dyes. The mass of synthetic colorants used by this industry is estimated at the level of 1 ÷ 3 × 105 tons, in comparison with the total annual consumption of around 7 × 105 tons worldwide. Synthetic dyes are relatively easy to detect but difficult to eliminate from wastewater and surface water ecosystems because of their aromatic chemical structure. It should be highlighted that the relatively high stability of synthetic dyes leads to health and ecological concerns due to their toxic, mutagenic, and carcinogenic nature. Currently, removal of such chemicals from wastewater involves various techniques, including flocculation/coagulation, precipitation, photocatalytic degradation, biological oxidation, ion exchange, adsorption, and membrane filtration. In this review, a number of classical and modern technologies for synthetic dye removal from industry-originated wastewater were summarized and discussed. There is an increasing interest in the application of waste organic materials (e.g., compounds extracted from orange bagasse, fungus biosorbent, or green algal biomasses) as effective, low-cost, and ecologically friendly sorbents. Moreover, a number of dye removal processes are based on newly discovered carbon nanomaterials (carbon nanotubes and graphene as well as their derivatives).