Technological advancements in high-throughput sequencing have lead to a tremendous increase in the amount of genomic data produced. With the cost being down to 2,000 USD for a single human genome, sequencing dozens of individuals is a task that is feasible even for smaller project or organizations already today. However, generating the sequence is only one issue; another one is storing, managing, and analyzing it. These tasks become more and more challenging due to the sheer size of the data sets and are increasingly considered to be the most severe bottlenecks in larger genome projects. One possible countermeasure is to compress the data; compression reduces costs in terms of requiring less hard disk storage and in terms of requiring less bandwidth if data is shipped to large compute clusters for parallel analysis. Accordingly, sequence compression has recently attracted much interest in the scientific community. In this paper, we explain the different basic techniques for sequence compression, point to distinctions between different compression tasks (e.g., genome versus read compression), and present a comparison of current approaches and tools. To further stimulate progress in genome compression research, we also identify key challenges for future systems.Keywords: genome compression, read compression, survey Key messages of the article:• Overview of trends in genome compression: bit manipulation, dictionarybased, statistical, and referential compression schemes• Wide ranges of compression performance (compression ratio, compression time, memory requirements)• Comparing compression schemes for evaluation purposes is difficult• Many minor improvements in recent contributions