Nowadays, breakthroughs in molecular biology are happening at an unprecedented rate. One of them is the ability to engineer transgenic animals. A transgenic animal is one whose genome has been changed to carry genes from another species or to use techniques for animal genome editing for specific traits. Animal features can be changed by purposefully altering the gene (or genes). A mouse was the first successful transgenic animal. Then pigs, sheep, cattle, and rabbits came a few years later. The foreign-interested genes that will be used in animal transgenic techniques are prepared using a variety of methods. The produced gene of interest is placed into a variety of vectors, including yeast artificial chromosomes, bacterial plasmids, and cosmids. Several techniques, including heat shock, electroporation, viruses, the gene gun, microinjection, and liposomes, are used to deliver the created vector, which includes the interesting gene, into the host cell. Transgenesis can be carried out in the gonads, sperm, fertilized eggs, and embryos through DNA microinjection, retroviruses, stem cells, and cloning. The most effective transgenic marker at the moment is fluorescent protein. Although transgenesis raises a number of ethical concerns, this review concentrates on the fundamentals of animal transgenesis and its usage in industry, medicine, and agriculture. Transgenesis success is confirmed by the integration of an antibiotic resistance gene, western and southern blots, PCR, and ELISA. If technology solves social and ethical problems, it will be the most promising in the future.