The warp speed limit was created in the wake of the Star Trek TNG episode "Force of Nature" and reduced all non critical travel to a factor of warp 5. But this limit was soon discarded from the shows going on without being addressed so let's take a look at the tale as technology unfolded in the shows using beta apocrypha to add details.

Star Trek Online developed by Cryptic Studios and Perfect World.
Star Trek Picard/Strange New Worlds/Lower Decks/Enterprise/Voyager/Deep Space Nine/Discovery and The Next Generation are all owned by Paramount Pictures/CBS and distributed by CBS.
This Video is for critical purposes with commentary.