Synthesis of DNA in eukaryotes is less well understood, but the process appears to be basically the same as in prokaryotes, with a few notable exceptions. For one thing, eukaryotic DNA is complexed with histones to form chromatin. Every round of replication, therefore, requires that the histones be removed, then replaced after replication is complete. This requirement understandably slows the whole replication process down.
Eukaryotic cells are also much more complex than prokaryotes, because they contain organelles such as mitochondria and chloroplasts (in plants) that contain their own DNA, which must also be replicated. Eukaryotic cells therefore have more than three DNA polymerases; there have been five DNA polymerases identified so far.
Eukaryotes have another difference: eukaryotic chromosomes are linear, rather than circular as in prokaryotes.
DNA Replication: Summary of Key Points