This chart made by Toby Ord shows four things:
• Everything we can observe now is the ‘observable universe’.
• Everything we can ever observe if we stay here is the ‘eventually observable universe’.
• Everything we can ever observe if we send spacecraft out in every direction at all speeds slower than light is the ‘ultimately observable universe’.
• Everything those spacecraft can ever affect is the ‘affectable universe’.
His chart is drawn in funny coordinates where a galaxy at rest moves straight up the page and light moves at 45° angles. The Big Bang is the horizontal line at the bottom, and the infinite future is the horizontal line at top. The expansion of the universe is hidden in these coordinates!
How big are these four things?
• When we observe distant galaxies we see what they were like long ago, when they were closer. Those galaxies now form a ball of radius 46 billion light years in diameter. So people say the radius of the observable universe is 46 billion light years. But beware: we can’t see what those galaxies look like now.
• The galaxies in the eventually observable universe now form a ball of radius 63 billion light years.
• The galaxies in the ultimately observable universe now form a ball of radius 80 billion light years.
• The galaxies in the affectable universe now form a ball of radius 16 billion light years.
These figures change with time. For example, shortly after the Big Bang the radius of the affectable universe was 63 billion light years. It has now shrunk to 16 billion light years. 90% of the galaxies we could in theory once reach—if we could have started right away—are lost to us now!
Of course, all these numbers are based on our current cosmology, which says that as the universe expands and ordinary matter thins out, the effect of dark energy becomes more important, and the universe starts expanding almost exponentially. If our theory of cosmology is wrong then these numbers are wrong!
You might wonder why the affectable universe has a finite radius even though the universe will last forever in our current theory. The reason is that because the universe is expanding faster and faster, it’s impossible to catch up with distant galaxies. So the only galaxies we can reach are those that are less than 16 billion light years away now.
For more, read Toby Ord’s paper:
• Toby Ord, The edges of our Universe.
and read my earlier blog post on this subject:
Azimuth 
The traditional names for the boundaries of the first three, in the order above, are “particle horizon”, “event horizon”, and “absolute horizon”. There was some genuine confusion until everything was cleared up by Wolfgang Rindler:
https://ui.adsabs.harvard.edu/abs/1956MNRAS.116..662R/abstract
If the above doesn’t work, try this.
If you want to see how those quantities depend on the cosmological model, check out this landmark paper.
If you read one paper on relativistic cosmology, that should be it.
I see that the links don’t work, even if I write them explicitly as HTML links. Probably because WordPress gets confused by dots in the URLs. So just copy the text of the link into a browser. The first is visible above. The second is https://ui.adsabs.harvard.edu/abs/1966MNRAS.132..379S/abstract
Roger Penrose uses conformal diagrams a lot in some of his books, and it took me a minute to wrap my head around them. They get interesting and more complex when illustrating things like black/white holes or more theoretical aspects of cosmology. They’re sort of like the more familiar spacetime diagrams, where light moves at a 45° angle, but rather different in their treatment of space (such as in how the BB is an infinite horizontal line). They can also illustrate how events far enough away can never affect us.