Although traditionally viewed as streamlined and simple, discoveries over the last century have revealed that viruses can exhibit surprisingly complex physical structures, genomic organization, ecological interactions, and evolutionary histories. Viruses can have physical dimensions and genome lengths that exceed many cellular lineages, and their infection strategies can involve a remarkable level of physiological remodeling of their host cells. Virus–virus communication and widespread forms of hyperparasitism have been shown to be common in the virosphere, demonstrating that dynamic ecological interactions often shape their success. And the evolutionary histories of viruses are often fraught with complexities, with chimeric genomes including genes derived from numerous distinct sources or evolved de novo. Here we will discuss many aspects of this viral complexity, with particular emphasis on large DNA viruses, and provide an outlook for future research.