Restriction endonucleases are enzymes that cut DNA molecules at specific sites, playing a crucial role in genetic engineering by allowing for the manipulation and cloning of genes. These enzymes recognize specific sequences of nucleotides and make precise cuts in the DNA, enabling the insertion of foreign genes into vectors. Other enzymes like DNA ligase, DNA polymerase, and reverse transcriptase are involved in other processes but do not perform the cleavage of DNA at specific sites.