The growing awareness of environmental issues and the pursuit of sustainable materials have sparked a substantial surge in research focused on biodegradable materials, including fibers. Within a spectrum of fabrication techniques, melt-spinning has emerged as an eco-friendly and scalable method for making fibers from biodegradable plastics (preferably bio-based), intended for various applications. This paper provides a comprehensive overview of the advancements in the realm of melt-spun biodegradable fibers. It delves into global concerns related to micro- and nanoplastics (MNPs) and introduces the concept of biodegradable fibers. The literature review on melt-spun biodegradable monofilaments and multifilaments unveils a diverse range of polymers and copolymers that have been subjected to testing and characterization for their processing capabilities and the performance of the resultant fibers, particularly from mechanical, thermal, and biodegradation perspectives. The paper discusses the impact of different factors such as polymer structure, processing parameters, and environmental conditions on the ultimate properties, encompassing spinnability, mechanical and thermal performance, and biodegradation, with schematic correlations provided. Additionally, the manuscript touches upon applications in sectors such as clothing, technical textiles, agriculture, biomedical applications, and environmental remediation. It also spotlights the challenges encountered in the commercialization of these fibers, addresses potential solutions, and outlines future prospects. Finally, by shedding light on the latest developments, challenges, and opportunities in the field, this review endeavors to stimulate further innovation and adoption of biodegradable fibers. It seeks to unlock their potential and contribute to the realization of a more environmentally conscious society.