The examination of patient data, which may contain personally identifiable information, is a common part of biomedical research. If these data are misused, it could result in the disclosure of private patient information, which would put the patients' right to privacy at risk. The challenge of protecting the privacy of patients in an era dominated by big data has garnered a growing amount of attention in recent years. There have been a lot of different privacy approaches created to protect against different attack models. In the context of research in biomedicine, this publication provides a review of pertinent subjects. It is discussed how technology can protect privacy, particularly in relation to record linking, synthetic data production, and the privacy of genomic data. In addition to this, we conduct an analysis of the ethical implications of the privacy of big data in biomedicine and we emphasise the obstacles that lie ahead for future research pathways aimed at strengthening data privacy in biomedical investigations. Both of these topics are covered in detail throughout this article. After the paper was first published, it was highlighted in the publication Biomedical Research.