If you are considering dark matter, after all these technological advancements, we could observe only 4% of the universe. The rest is dark matter which we cannot even detect yet.
Follow the source for more about this case.
If you mean how far out can we see, the answer is pretty close to the observable wall and/or particle horizon using Hubble Space Telescope. It is only physically possible to see so far because after a point the space is receding from you faster than the speed of light because of the expansion of the universe. Another way to think about it: photons from the objects you are seeing have had to travel against expanding space for ~13Byr, for some of their journey, even at the speed of light, they were being carried away from us before they started making actual progress.
Even if this were not the case, you would hit the point in history when the universe was optically thick because photons had not decoupled from matter and so you wouldn't be able to see anything in this regime.
However this carries the caveat that we can only see extremely large scale structures such as galaxies/clusters of galaxies. So what we see are extremely coarse snapshots from long ago.
I guess you could say we have a rough outline of the observable universe at best, with a pretty decent underlying model to explain what has been observed so far, but we really do not understand large components such as dark energy (some 73% of what "makes-up" our universe), and really we only understand something like 10-15% of normal matter, which combined with dark matter makes up the other 27% of the universe. The 3rd component, relativistic or radiation is essentially negligible.
Going by this logic, we understand ~15% out of 27% of the universe fairly well. We can hand-waivingly explain the rest of matter, which is to say we can describe some properties of dark matter but not intrinsically understand what it is.
We have absolutely no idea what Dark Energy is, other than an ability to ascribe a mathematical value to it based on observations.
So at best we have outlined "everything", understand slightly better about 27%, all matter, and really understand about 15% of that 27%, normal matter.