Computer-assisted studies of structure, function, and evolution of viruses remains a neglected area of research. The attention of bioinformaticians to this interesting and challenging field is far from commensurate with its medical and biotechnological importance. It is very telling that out of over 200 talks held at ISMB 2013, the largest international bioinformatics conference, only one presentation explicitly dealt with viruses. In contrast to many broad, established and well organized bioinformatics communities (e.g. structural genomics, ontologies, next-generation sequencing, expression analysis), research groups focusing on viruses can probably be counted on the fingers of two hands. The purpose of this review is to increase awareness among bioinformatics researchers about the pressing needs and unsolved problems of computational virology. We focus primarily on RNA viruses that pose problems to many standard bioinformatics analyses due to their compact genome organization, fast mutation rate, and low evolutionary conservation. We provide an overview of tools and algorithms for handling viral sequencing data, detecting functionally important RNA structures, classifying viral proteins into families, and investigating the origin and evolution of viruses.