For years, certain scientists have been trying to bring back extinct species - a process called de-extinction - but as of 2015 most have been unsuccessful. In theory, it is possible to bring back an extinct species, but it also brings up ethical questions and further complications that go beyond simply replicating an animal.
You might compare de-extinction to the movie Jurassic Park. Samples of DNA are saved from an extinct species, and that DNA is used to clone a new animal. In 2003, scientists tried to de-extinct a Pyrenean ibex by using mountain goats as surrogate mothers. All of their efforts failed, and when they tried again in 2009, one ibex was born for seven minutes before dying of a lung complication.
Similarly, as of April 2013 scientists in Russia and South Korea planned to resurrect the woolly mammoth using an Asian elephant as a surrogate mother. This raised ethical issues, however, about the well-being of the mother and what would happen if or when a new woolly mammoth was born.
Some scientists say that conservation of existing species, not de-extinction, should be the focus of biologists. After all, no one knows how a previously-extinct species would survive in a new environment, or how capable it would be of repopulating enough to bring the species back for good.
One thing is certain - many scientists feel that they've only scratched the surface of how genetics might help bring back old species. While the efforts and goals of these scientists will not go away (and they'll likely become more common), the ethical debate over the why will continue and evolve.