What is the farthest we can see into the universe?
It depends. In some areas, far-away stuff is obscured by obstacles in the foreground. In other places, we can see almost all the way to the earliest (and furthest-away) galaxies, like in the Hubble Deep Field image: 



The very earliest objects have so much redshift they disappear out of view for visible-light telescopes. That's where the JWST comes in: because it's an infrared telescope, it can capture objects that have too much redshift to be visible in a visible-light telescope. 

Advances help us see more in other ways too. Gaia data revealed some small nearby galaxies which are mostly obscured by our own galaxy.