Clinical trial eligibility matching is a critical yet often labor-intensive and error-prone step in medical research, as it ensures that participants meet precise criteria for safe and reliable study outcomes. Recent advances in Natural Language Processing (NLP) have shown promise in automating and improving this process by rapidly analyzing large volumes of unstructured clinical text and structured electronic health record (EHR) data. In this paper, we present a systematic overview of current NLP methodologies applied to clinical trial eligibility screening, focusing on data sources, annotation practices, machine learning approaches, and real-world implementation challenges. A comprehensive literature search (spanning Google Scholar, Mendeley, and PubMed from 2015 to 2024) yielded high-quality studies, each demonstrating the potential of techniques such as rule-based systems, named entity recognition, contextual embeddings, and ontology-based normalization to enhance patient matching accuracy. While results indicate substantial improvements in screening efficiency and precision, limitations persist regarding data completeness, annotation consistency, and model scalability across diverse clinical domains. The review highlights how explainable AI and standardized ontologies can bolster clinician trust and broaden adoption. Looking ahead, further research into advanced semantic and temporal representations, expanded data integration, and rigorous prospective evaluations is necessary to fully realize the transformative potential of NLP in clinical trial recruitment.