Genome packaging is a fundamental process in a viral life cycle. Many viruses assemble preformed capsids into which the genomic material is subsequently packaged. These viruses use a packaging motor protein that is driven by the hydrolysis of ATP to condense the nucleic acids into a confined space. How these motor proteins package viral genomes had been poorly understood until recently, when a few X-ray crystal structures and cryo-electron microscopy (cryo-EM) structures became available. Here we discuss various aspects of genome packaging and compare the mechanisms proposed for packaging motors on the basis of structural information.