Cellular DNA replication requires efficient copying of the double-stranded chromosomal DNA. The leading strand is elongated continuously in the direction of fork opening, whereas the lagging strand is made discontinuously in the opposite direction. The lagging strand needs to be processed to form a functional DNA segment. Genetic analyses and reconstitution experiments identified proteins and multiple pathways responsible for maturation of the lagging strand. In both prokaryotes and eukaryotes the lagging-strand fragments are initiated by RNA primers, which are removed by a joining mechanism involving strand displacement of the primer into a flap, flap removal, and then ligation. Although the prokaryotic fragments are ~1200 nucleotides long, the eukaryotic fragments are much shorter, with lengths determined by nucleosome periodicity. The prokaryotic joining mechanism is simple and efficient. The eukaryotic maturation mechanism involves many enzymes, possibly three pathways, and regulation that can shift from high efficiency to high fidelity.