This research paper explores the development of Named Entity Recognition (NER) systems, particularly emphasising its application in the medical field. It summarises the mathematical foundations of NER, traditional and advanced methods, and the difficulties encountered in several industries. Within this exploration, the paper encompasses rule-based, statistical learning-based, and deep learning-based approaches to NER. The paper explores traditional methods and advanced techniques, including handcrafted rule-based systems, statistical learning algorithms, and deep learning architectures like LSTMs and BiLSTMs. The study includes a comparative analysis of popular NLP libraries (TensorFlow, SpaCy, Stanford NLP, and OpenNLP (Apache)) and evaluates NER models on a medical dataset. In the evaluation, the SpaCy library model comes out on top, outperforming other models in terms of performance accuracy and yielding exceptional results. The study's main conclusions are that the SpaCy library model outperforms other models in medical NER tasks and that resolving data issues is crucial to obtaining finer-grained entity recognition. This paper also addresses the future developments in NER, emphasizing the importance of addressing data issues and achieving finer-grained entity recognition.