Hi there 
I was wondering if there is any benifit to fighting with a 1h weapon and no shield, like a duelist?
I've always thought it was very cool, but it just seems plain bad.
Is there any feat or something that i missed to make this build legit?
(i know i can do it anyway, but that will just make a very poor fighter ^^)
You can cast a spell with your free hand, that can be handy for some characters. It lets you grapple opponents any time you like.
But for the most part, there's no obvious reason to forgoe using one of your limbs.
The only things that explicitly reference this style are the Duelist fighting style (which helps up the damage a bit, but not by much) and the Defensive Duelist feat (which is nifty, but won't help take down foes faster, when taking down foes faster might have the same effect). You can also make use of any weapon-related abilities found on sword-and-board fighters (since you're still fighting with a 1-H weapon), and some of those on dual wielders (since, again, you're still using the same type of weapon).
There's two hidden benefits, though - you have a hand free, meaning you can cast spells without any hassles at all (there are some weird interactions with material components, foci (even those holy symbols on shields), and somatic components, and you won't need War Caster or anything to do it), and that free hand also helps with unusual combat techniques like grappling. (I still want to toy around with this, seeing if I can get a character working who'll grab-and-stab, but I haven't looked into it yet.) The free hand also helps in oddball situations, such as if you're blown off a cliff and try to reach out and grab a rock or something to stop your fall (good luck doing that with a shield), or if you're using something other than a weapon in that off-hand (i.e. a gladiator-style net or a lasso). If you happen to have a magic item, you can also hold that in your other hand and make use of it, actions depending.
However, the thing to note is that 5e's spread of power isn't as wide as previous editions have been, particularly if feats aren't used or if the problematic ones are regulated. The amount "behind" that you'd be by adopting a dueling style isn't far enough behind to justify "very poor" unless your definition of "very poor" is "1 or more points behind the absolute maximum" - and that's not a reasonable definition by most standards.
Tempest_Stormwind wrote:
As Raijin411 points out, the duelist style (RAW) does allow you to wield a shield and get the benefit. Our group discussed whether to house rule a 'correction', but realized that the +2 to damage doesn't equal the improved damage you're going to get from a second weapon (or on average, by rerolling 1s and 2s on a great weapon). The one thing that I would point out is that if someone else at your table has successfully convinced the DM that a shield is a weapon (so they can shield bash as an improvised weapon using a bonus action), then this decision may work against what many people consider to be common sense (that the Duelist style works with a shield)
The reason to fight one handed is really flexibility. If you're a caster without the Warcaster feat, you often need a hand free. You could also Attack with your action (gaining your +2), and then use your bonus action to draw and throw a dagger.
Try the Tavern Brawler feat. Hit with your fist, grapple the target as a Bonus Action, hit it with your weapon again with your extra attacks. This is a protective build, since you prevent the enemy you're targeting from moving away from you and it does stack neatly with the Grappler feat, which would give you advantage to your attack rolls after a successful grapple. Even though it's kinda specific, this build is seriously powerful in dungeoncrawls and other places with not much space. If you face a lot of huge or larger creatures it won't be as helpful, of course.
But even then there are some benefits of having a hand free, like disarming your target and pick up its weapon or the fact, that you can draw a weapon and throw it with your free hand more often. And you you rather pick the Defense fighting style, you can alternate between one and two hands with a versatile weapon depending on your needs without worrying.
Torch.
It will have situational benefits.
For example:
At a formal event where dress weapons are allowed but armour and shields are not.
While having a meal (shield is probably leaning against a wall nearby).
While on a boat, where the spare hand is needed to hang on to ropes to avoid falling overboard.
How often you use these will depend on the campaign. I imagine that in a "sea buccanner" campaign, the feat will be very useful.