In recent years, whole genome sequencing (WGS) evolved from a futuristic-sounding research project to an increasingly affordable technology for determining complete genome sequences of complex organisms, including humans. This prompts a wide range of revolutionary applications, as WGS is a promising means for improving modern healthcare and providing a better understanding of the human genome, in particular its relation to diseases and response to treatments. However, this progress raises worrisome privacy and ethical issues, since, besides uniquely identifying its owner, the genome contains a treasure trove of highly personal and sensitive information. In this article, after summarizing recent advances in genomics, we discuss some important privacy issues associated with human genomic information and identify a number of particularly relevant research challenges.