Would be possible to apply genetic changes (like splicing in a radiation hardening gene) to an adult human? With near future technology, like advanced forms of CRISPR? Or can things like that only be applied t unborn infants?
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Yes but it's much harder and the effects can be limited and much slower.

**Genetic Surgery**

Enough engineered viruses can change the DNA but can be limited on changing physical structures.

Here's an [example](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4401361/) where viral surgery was used to repair genetic deafness in mice

If you are making large physical changes, it might take a very long time to take effect if at all.
[Gene Therapy](https://en.wikipedia.org/wiki/Gene_therapy)
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With the gene therapy, is possible to modify the DNA of a born creature using Virus, Retrovirus, Adenovirus, Non-Virus or others as a Vector. (Surprisingly, the Spanish Wikipedia has more information about different vectors). 

This [vectors](https://en.wikipedia.org/wiki/Vectors_in_gene_therapy) are programmed to modify the DNA structure of alive cells from the host.

At the moment it's quite dangerous or ineffective this gene therapy, but in the future, with the boom of genetical manipulation, it will no longe be a problem.