The growing awareness of pollutants from the textile industry and synthetic dyes has led to a revolutionary shift in the textile sector towards sustainability. At the heart of this movement is the search for eco-friendly alternatives to conventional synthetic dyes and mordants, which often pose serious risks to human health and the environment. This search is progressing rapidly. Research findings have shown that natural dyes—traditionally derived from plant, animal, or mineral sources—have become promising alternatives to synthetic dyes due to their environmental compatibility and sustainability. Scientists are increasingly focused on understanding the chemical structures of these dyes, developing a wider range of color shades, discovering new natural dye sources, and overcoming the limitations of natural dyes. This article reviews the results of extensive research on the latest developments in identifying eco-friendly dye sources and bio-based mordants, as well as strategies for reducing the environmental impact of mineral mordants. It also presents the latest achievements in various dye extraction methods, including modern technologies such as ultrasonic extraction, supercritical fluid extraction, and microwave-assisted extraction, in comparison to traditional methods. The efficiency and functional properties of natural dyes are also discussed, including medicinal benefits, deodorizing effects, antibacterial and antimicrobial properties, moth repellence, and UV protection. Research results indicate that, despite the growing application of natural dyes across different scientific fields and the documented contributions of countries and researchers in this domain, there is still a need for more in-depth studies to adapt natural dyes to dyeing machinery and to improve dyeing efficiency and quality.