Plant pathogenic geminiviruses have been proliferating worldwide and have, therefore, attracted considerable scientific interest during the past three decades. Current knowledge concerning their virion and genome structure, their molecular biology of replication, recombination, transcription, and silencing, as well as their transport through plants and dynamic competition with host responses are summarized. The topics are chosen to provide a comprehensive introduction for animal virologists, emphasizing similarities and differences to the closest functional relatives, polyomaviruses and circoviruses.