Uracil-DNA glycosylases are ubiquitous enzymes, which play a key role repairing damages in DNA and in maintaining genomic integrity by catalyzing the first step in the base excision repair pathway. Within the superfamily of uracil-DNA glycosylases family I enzymes or UNGs are specific for recognizing and removing uracil from DNA. These enzymes feature conserved structural folds, active site residues and use common motifs for DNA binding, uracil recognition and catalysis. Within this family the enzymes of poxviruses are unique and most remarkable in terms of amino acid sequences, characteristic motifs and more importantly for their novel non-enzymatic function in DNA replication. UNG of vaccinia virus, also known as D4, is the most extensively characterized UNG of the poxvirus family. D4 forms an unusual heterodimeric processivity factor by attaching to a poxvirus-specific protein A20, which also binds to the DNA polymerase E9 and recruits other proteins necessary for replication. D4 is thus integrated in the DNA polymerase complex, and its DNA-binding and DNA scanning abilities couple DNA processivity and DNA base excision repair at the replication fork. The adaptations necessary for taking on the new function are reflected in the amino acid sequence and the three-dimensional structure of D4. An overview of the current state of the knowledge on the structure-function relationship of D4 is provided here.