Composting is the most adaptable and fruitful method for managing biodegradable solid wastes; it is a crucial agricultural practice that contributes to recycling farm and agricultural wastes. Composting is profitable for various plant, animal, and synthetic wastes, from residential bins to large corporations. Composting and agricultural waste management (AWM) practices flourish in developing countries, especially Pakistan. Composting has advantages over other AWM practices, such as landfilling agricultural waste, which increases the potential for pollution of groundwater by leachate, while composting reduces water contamination. Furthermore, waste is burned, open-dumped on land surfaces, and disposed of into bodies of water, leading to environmental and global warming concerns. Among AWM practices, composting is an environment-friendly and cost-effective practice for agricultural waste disposal. This review investigates improved AWM via various conventional and emerging composting processes and stages: composting, underlying mechanisms, and factors that influence composting of discrete crop residue, municipal solid waste (MSW), and biomedical waste (BMW). Additionally, this review describes and compares conventional and emerging composting. In the conclusion, current trends and future composting possibilities are summarized and reviewed. Recent developments in composting for AWM are highlighted in this critical review; various recommendations are developed to aid its technological growth, recognize its advantages, and increase research interest in composting processes.