This already happens all the time, it's what a virus does. It infects cells and subverts them by changing the cells genetics to produce new copies of the virus. Those same pathways can be used by us to modify the virus and then use it to produce controlled modifications in humans.
There are a number of problems and limitations with the method at the moment though, the biggest being that we have very limited control. We can set up the payload in the virus but it is very hard to make sure it delivers it to the right place in the genome, so it could end up writing junk, making things worse, etc.
It's also hard to just deliver it to the cells that need it if you have a localized problem. For example if you have a problem in your heart then in theory you could deliver a fix but isolating the fix to just the heart is hard. The changes you want to happen in the heart could also happen and produce unwanted side effects elsewhere in the body.
One huge worry is cancer, no-one is quite sure what effects gene therapy is going to have on cells and what the risks of it triggering serious conditions like cancer is.
The effects these changes can have are also limited by the fact that they are working with what has already grown. For example you could take someone 5' tall and put the genes to grow to 6' tall into that person. However they have already grown, so the genes will not achieve anything. You would need to somehow both put the genes for an extra foot of height in and also re-kickstart the growing process.
Basically the genes are the blueprint for the body, changing ongoing process is one thing but changing something that has already happened is much harder.
You should also consider immune rejection, if you change things too radically then the immune system might detect the modified cells as foreign and attack them. This could be fatal just by itself.