Viruses constitute the largest group of emerging pathogens, and geminiviruses (plant viruses with circular, single-stranded DNA genomes) are the major group of emerging plant viruses. With their high potential for genetic variation due to mutation and recombination, their efficient spread by vectors, and their wide host range as a group, including both wild and cultivated hosts, geminiviruses are attractive models for the study of the evolutionary and ecological factors driving virus emergence. Studies on the epidemiological features of geminivirus diseases have traditionally focused primarily on crop plants. Nevertheless, knowledge of geminivirus infection in wild plants, and especially at the interface between wild and cultivated plants, is necessary to provide a complete view of their ecology, evolution, and emergence. In this review, we address the most relevant aspects of geminivirus variability and evolution in wild and crop plants and geminiviruses’ potential to emerge in crops.