Biomedical research often involves studying patient data that contain personal information. Inappropriate use of these data might lead to leakage of sensitive information, which can put patient privacy at risk. The problem of preserving patient privacy has received increasing attentions in the era of big data. Many privacy methods have been developed to protect against various attack models. This paper reviews relevant topics in the context of biomedical research. We discuss privacy preserving technologies related to (1) record linkage, (2) synthetic data generation, and (3) genomic data privacy. We also discuss the ethical implications of big data privacy in biomedicine and present challenges in future research directions for improving data privacy in biomedical research.