Research on Information Retrieval (IR) focuses on developing advanced methods to enhance the accuracy, efficiency, and fairness of retrieving relevant information from large datasets. Recent studies have introduced models like CSPLADE, which leverage learned sparse representations with causal language models to improve training stability and reduce index sizes, and frameworks such as ECLIPSE, which utilize contrastive dimension importance estimation with pseudo-irrelevance feedback to refine document relevance. Methods like FAIR-QR aim to ensure fairness by retrieving documents from underrepresented groups while maintaining interpretability, and the integration of Large Language Models (LLMs) into IR systems further enhances retrieval performance and user experience. Collectively, these innovations advance IR by optimizing search effectiveness, promoting equity, and incorporating AI-driven intelligence to meet the demands of modern information access.