Recent developments in a variety of sectors, including health care, research and the direct-to-consumer industry, have led to a dramatic increase in the amount of genomic data that are collected, used and shared. This state of affairs raises new and challenging concerns for personal privacy, both legally and technically. This Review appraises existing and emerging threats to genomic data privacy and discusses how well current legal frameworks and technical safeguards mitigate these concerns. It concludes with a discussion of remaining and emerging challenges and illustrates possible solutions that can balance protecting privacy and realizing the benefits that result from the sharing of genetic information.