Replication of DNA takes place in the nucleus in eukaryotic cells, as this is where the chromosomal DNA is stored and maintained. The process begins with the separation of the two strands of the DNA double helix, followed by the synthesis of new complementary strands by various enzymes. In prokaryotic cells, DNA replication takes place in the cytoplasm since prokaryotes lack a defined nucleus. In both cases, the process involves a series of tightly regulated steps, including the initiation at specific replication origins, elongation of the new DNA strands, and the final termination once replication is complete.