The rapid focus on sustainability in the textile and fashion industry has led to the development of biodegradable and compostable fibres. These materials, derived from natural sources, are shaping the industry by offering potential eco-friendly solutions that reduce environmental threats and challenges when disposed. Biodegradable fibres such as wool, silk, organic cotton, and hemp, among others, can decompose naturally without solvents, while compostable fibres like bio-engineered and polylactic acid materials can be broken down under certain conditions into compost within the environment. Technological advances for compostable fibres are emerging as potential alternatives to synthetics, which are long-lasting pollutants in the environment. The utilisation of biodegradable fibres effectively contributes to the sustainability and circularity drive in the industry, reducing carbon footprint and safeguarding the ecosystem. Thus, supporting sustainable practices responsible for waste management and consumption within the value chain. Despite these benefits, ethical considerations regarding the sourcing and application of these fibres could influence social equity and responsibility, potentially limiting environmental sustainability. In this chapter, we discuss the types, analytical methods, and properties of biodegradable and compostable fibres. The core application areas of these materials are also examined to provide an overview of advancing circularity and sustainability for a responsible industry. Additionally, challenges such as disposal infrastructure, cost-efficiency, and scalability are discussed, which hinder the widespread use and adoption of these materials for the benefit of industry and the environment. The chapter concludes with insights into promising areas for future research and policy development to significantly contribute to a responsible and sustainable future in the textile and fashion industry.