Advances in genomic research have created new privacy challenges. This scoping review analyzes the risks associated with the processing, storage, and sharing of genomic data including epigenetics, and examines current privacy protection strategies. It also attempts to identify research gaps in this area. Using the PRISMA methodology, 37 relevant studies were identified and analyzed. The results of the risk assessment can be grouped into four main themes: Risks posed by processing of functional genomic data, sharing of genomic data, patient (re-)identification, and dividuality, i.e. the extending of privacy risks to blood relatives. The identified risk mitigation strategies were systematically categorized into five classes: pre-release measures, governance, secure data processing and exchange, access restriction and transparency, anonymization and masking. However, there are some important research gaps that still need to be addressed. The current literature neglects to assess the likelihood of potential breaches and tends to focus only on assessing possible scenarios of privacy risks. It also mainly fails to assess the role of contextualized data and the effectiveness of policies and governance systems with respect to privacy risks.