We have reconstituted a eukaryotic leading/lagging strand replisome comprising 31 distinct polypeptides. This study identifies a process unprecedented in bacterial replisomes. While bacteria and phage simply recruit polymerases to the fork, we find that suppression mechanisms are used to position the distinct eukaryotic polymerases on their respective strands. Hence, Pol ε is active with CMG on the leading strand, but it is unable to function on the lagging strand, even when Pol δ is not present. Conversely, Pol δ-PCNA is the only enzyme capable of extending Okazaki fragments in the presence of Pols ε and α. We have shown earlier that Pol δ-PCNA is suppressed on the leading strand with CMG (Georgescu et al., 2014). We propose that CMG, the 11-subunit helicase, is responsible for one or both of these suppression mechanisms that spatially control polymerase occupancy at the fork. DOI: http://dx.doi.org/10.7554/eLife.04988.001, eLife digest Cells must replicate their DNA before they divide so that the newly formed cells can each receive a copy of the same genetic material. DNA replication requires complex molecular machinery called a replisome, which comprises multiple proteins, enzymes, and other molecules. First, an enzyme called a helicase starts to unwind the double-stranded DNA into two single strands. This process continues while other enzymes, called polymerases, use the exposed single strands as templates to make complementary new strands of DNA. One of these new strands is built continuously and called the ‘leading strand’. The other newly forming strand—the ‘lagging strand’—is made in the opposite direction, as a series of short fragments that are later joined together. The replisomes in bacterial cells have been well studied, but many researchers are investigating the composition of the replisome in animals, plants, and fungi (collectively called eukaryotes). Now, Georgescu et al. have essentially rebuilt a eukaryotic replisome from 31 different proteins in a test tube and confirmed that it can make both leading and lagging DNA strands—just like in a normal cell. Further experiments revealed that the polymerase enzyme that operates on the leading strand cannot work on the lagging strand and vice versa. This exclusivity is unique to eukaryotic DNA replication, as bacterial polymerases can use either DNA strand as a template. Georgescu et al. then found that the eukaryotic polymerases are actively prevented from copying the ‘wrong’ strand of DNA and suggest that the helicase enzyme that unwinds the DNA might be behind this activity. Important future studies must now address how the replisome deals with obstacles created by certain DNA-binding proteins and damaged DNA and how it interfaces with the molecules that control cell division and DNA repair. DOI: http://dx.doi.org/10.7554/eLife.04988.002