The system is mostly the same as it was in Borderlands 1: Beating playthrough one does nothing except unlock playthrough two ("True Vault Hunter Mode"), beating playthrough 2 scales enemies and rewards to your level, unlocking playthrough 3 (if you're level 50, I believe). Playthrough 3 is new and scales to your level from the start.
True Vault Hunter Mode (playthrough 2-2.5)
Playthrough 2 is unlocked simply by beating Playthrough 1, and is identical to playthrough 1 until completion except with higher level requirements, higher level enemies and generally harder enemies.
Once you beat playthrough two, enemies scale to within 3 levels of you; some weak enemies (like Skag Pups) may be level 48, most enemies will be level 49-51, bosses will often be level 52, and occasionally enemies will even be 53. This is known as "playthrough 2.5" as it was in Borderlands 1.
Loot scales to within a couple levels; most drops will be level 49 or 50. Quest rewards scale to your level too; this is why it's important not to start certain side quests until playthrough 2.5, otherwise you'll miss out on the highest level rewards. Side quests scale to when you start the mission so don't take them too early, if you want a level 50 reward, wait until you've finished the main quest. Of course if the reward is green, you can go ahead and do it because the reward is junk anyway.
Note, without the UVHM DLC that it's still important to cap out your level, not just get to playthrough 2.5 before getting rewards, but as of right now the max level without the UVHM DLC is still 50, and it's hard not to be level 50 by the time you complete the second playthrough.
Ultimate Vault Hunter Mode (playthrough 3)
As of a patch April 2013, there is also now an Ultimate Vault Hunter Mode or playthrough 3, which is scaled to your level and much harder. It's mostly explained in these patch notes and this explanation:
- Ultimate Vault Hunter Mode is unlocked for a character once they have completed the main story missions in True Vault Hunter Mode and reached level 50.
- Unlike other playthroughs, Ultimate Vault Hunter Mode can be replayed multiple times with players able to reset their overall mission progress at any time from the Main Menu.
- No more tutorial missions -- characters in Ultimate Vault Hunter Mode begin in Southern Shelf with the "Cleaning Up the Berg" mission.
- While playing in Ultimate Vault Hunter Mode, enemies and bosses will scale according to the player's current level or, if playing with others, the highest-level player in that party.
-Gameplay changes in UVHM:
- Enemy health generally increased 4x.
- Enemies now have a moderate amount of health regeneration.
- Increased duration of slag damage multiplier effect.
- Upped the damage that slagged enemies take from 2x to 3x.
- Weapon swap speed increased to better facilitate slag use.
- Enemies now more likely to drop ammo.
- Loot Midgets are now "Legendary Loot Midgets" that can drop Legendary and other top-tier gear.
- Powerful new “Ancient” E-Tech relics and rare Pearlscent-grade weapons can be picked up in Ultimate Vault Hunter Mode.
Generally speaking, enemies are harder, have much more health, slag is much more effective, rare drops are increased and certain new E-Tech relics and Pearlescent (cyan colored) equips are avalible only in UVHM. The E-tech relics and Pearlescents are only availible in UVHM for people with the Ultimate Vault Hunter Upgrade pack ($5 DLC, included for free with the Season Pass).
Note that due to the increased difficulty and increased efficacy of Slag, UVHM is particularly suited to co-op play. Just like in "raid" boss fights, a Siren with Res is always useful.
To my knowledge there's no "playthrough 3.5" since the ".5" was always about enemies/loot that scale to your level. Playthrough 3 scales from the start so there's no extra post-playthrough for scaling.
Best Answer
You restart in True Vault Hunter Mode, the second difficulty. (Go to main menu, Select Character, re-select your character, and it should ask you which difficulty you want to play in).
TVHM is the same game, but starts at level 30, and ends at level 50. Also, some more difficult variations of enemies are introduced, like Armored Psychos. All elemental resistances and vulnerabilities are more pronounced - it is even more stupid now to shoot armor with fire, and fire does even more bonus damage to flesh. After you beat The Warrior in TVHM, entire game world (including first areas) is scaled to level 50 - this is informally known as "playthrough 2.5".
At the release of BL2, 50 was max level, so that's why Terramorphous is scaled to 50 even on Normal. Currently, there is also an Ultimate Vault Hunter Mode, the third difficulty (but I believe, you have to buy DLC to access that). UVHM spans from level 50 to level 61 or 72 (depending on DLC), and is even harder - enemies regenerate, but Slag now triples the incoming damage.