Scientists are working on developing a wooly mammoth-elephant hybrid, a "mammophant" (Devlin 2017). They would accomplish this by splicing together mammoth DNA recovered from preserved species with Asian elephant DNA using the CRISPR/Cas9 system, and then developing an embryo in an artificial womb (Devlin 2017). CRISPR/Cas9 is a gene editing system in which a protein, Cas9, is guided by a site-specific RNA molecule to a target site of DNA ("CRISPR/Cas9" n.d.). The Cas9 protein can make a single cut to disrupt and inactivate a gene, or two Cas9 proteins can cut selected DNA out and remove it, or the Cas9 system can even correct or insert a DNA sequence (CRISPR/Cas9 n.d.). The system is a modification of a bacterial strategy to target invading viruses: the bacteria "record" the viruses' DNA and then encode information about them in CRISPR arrays (The National Human Genome Research Institute, n.d.). If attacked again, the bacteria can target the viruses by transcribing the arrays into RNA, which, in combination with a Cas9 or similar protein, can then attack the viruses (The National Human Genome Research Institute, n.d.).
The current rationale for bringing wooly mammoths back as elephant-hybrids--apart from the fact that it would be cool--is that these creatures could serve as lawn-care specialists for the tundra, and possibly slow global warming (Devlin 2017). According to Dr. George Church, one of the scientists leading the project, wooly mammoths might help keep the tundra cooler by punching through the frozen layer around the ground, allowing cool air to circulate and keep the frozen ground frozen (Devlin 2017). This would help to keep greenhouse gases from escaping (Devlin 2017).
There are potential ethical and zoological difficulties and ecological problems, however. Matthew Cobb, a zoologist, points out that these are social animals, and scientists cannot guarantee a "mammophant" a herd (Devlin 2017). There are also possible unforeseen ecological consequences--the arctic tundra is not the same tundra the mammoths once inhabited. We can't be sure what consequences there could be for the environment or these animals if they were released. We don't know if they'd monopolize the land, or how whether we'd be prepared to help them survive in the wild.
It's unlikely that this method could be used for all extinct species as some species, such as jellyfish, preserve extremely poorly.
CRISPR/Cas9. (n.d.) CRISPR Theraputics. Retrieved from: http://www.crisprtx.com/gene-editing/crispr-cas9Devlin, H. (2017) Woolly mammoth on verge of resurrection, scientists reveal. The Guardian. Retrieved from: https://www.theguardian.com/science/2017/feb/16/woolly-mammoth-resurrection-scientists
The National Human Genome Research Institute. (n.d.) What are genome editing and CRISPR-Cas9? Retrieved from: https://ghr.nlm.nih.gov/primer/genomicresearch/genomeediting