Despite tremendous advances in high-resolution structure determination of virus particles, the organization of encapsidated genomes and their role during assembly are poorly understood. This article summarizes recent insights from structural, biochemical, and genetic analyses of icosahedral viruses that contain single-stranded, positive-sense RNA genomes. X-ray crystallography of several viruses in this category has provided tantalizing glimpses of portions of the packaged nucleic acid, contributing crucial information on how the genome might be folded within the virion. This information combined with theoretical considerations and data from molecular approaches suggests mechanisms by which coat proteins interact with genomic RNA to shape it into a conformation that is compatible with the geometry of the virion. It appears that RNA, in addition to its function as a repository for genetic information, plays an important structural role during assembly and can on occasion override the ability of the coat protein to form a particle with defined icosahedral symmetry.