Your question is somewhat incomplete in that it asks about the relationship of Genetic Engineering, without specifying relationship to what. Therefore, in the absence of a more precise understanding of your question, I am providing a brief general outline of genetic engineering and recombinant DNA.
Genetic Engineering is the modification of an organism by manipulation of its DNA. The organism's genome is altered by inserting synthetic genes or foreign DNA.
Recombinant DNA involves the use of laboratory techniques to produce sequences of amino acids not normally found in the DNA of a biologic organism. This form of molecular cloning produces artificial species of organisms.
Milestones of successful use of Recombinant DNA for Genetic Engineering are as follows:
1973: successful production of genetically altered bacteria
1982: first commercial production of insulin-producing bacteria
1994: first commercial production of genetically modified food
The first reference gives a more detailed explanation of methods of Genetic Engineering. The second explains recombinant DNA.