DNA replication takes place in the nucleus of eukaryotic cells and in the cytoplasm of prokaryotic cells, HowStuffWorks states. Reference explains that prokaryotes are organisms without a nucleus.
According to HowStuffWorks, DNA replication follows a similar process across all cells, whether bacterial or animal. DNA replication begins when the enzyme gyrase, gets the process started. Gyrase cuts the double-stranded DNA to prepare it for unravelling. Next, the enzyme helicase unzips the DNA. At this point, single-strand binding proteins keep the two halves of the double helix separated, during which time the enzyme polymerase pair nucleotides together. This process creates two double helices from one. While pairing nucleotides together, polymerase simultaneously proofreads the process to make sure that the pairing is correct, with the A bases being paired with the T bases and the G bases being paired only with the C bases. After the pairing is complete the enzyme ligase zips the DNA together into its double helix.
Reference.com points out that although prokaryotes have no nucleus in which DNA replication can take place, they contain ribosomes, which are organelles found in the cytoplasm that help with the process of DNA replication. Prokayrotes are organisms that include the domains of Bacteria and Archaea. All other life forms are classified in the eukaryotic domain.