It's often been said that the Klingons and Romulans kind of flipped attributes. In TOS the Klingons were the guys who were always plotting and started a lot of proxy conflicts, while the Romulans sort of had a code of honor (Well, at least the commander who looked like Sarek did).
However, starting with Star Trek III this seems to be turned on it's head. The Klingons now have cloaking devices for their own "Birds of Prey", and the honor thing starts to take some shape although it's not fully formed until TNG (I've read that the Romulans were the original villains of III, but changed to Klingons, possibly to avoid confusion with the Vulcans?). Once TNG rolls around the Romulans are the plotting ones behind the scenes.
There's some 'fanon' I think that the two had an alliance of sorts around the time of TOS's third season and the first movie, which explains why they had the Klingon ships in "Enterprise Inciddent"; but that at some point the alliance went sour and they became bitter enemies as we see in TNG.
Section 31 also played a role in "Into Darkness" as well, although an alternate version of course.