When wielding two light weapons or a dagger and one other weapon, you are two-weapon fighting. You gain the following benefits:
When you take the attack action, you may make a two-weapon attack in place of a regular weapon attack. Use the weapons’ combined weapon dice and the higher enhancement bonus (if either weapon has an enhancement bonus). This counts as a single weapon attack. If you take the attack action more than once on your turn due to having additional actions, such as from action surge or haste, you may use this feature once during each additional action. Any additional attacks gained from the Extra Attack class feature or similar benefits do not allow multiple Two-Weapon Strikes. Instead, you make each additional attack with a single weapon you are wielding.
You may treat your two weapons as a single weapon for the purpose of effects such as magic weapon and Warlock’s Blade Pact and for the purpose of drawing and sheathing and applying attack riders and damage.
So if wielding two short swords, your attack two weapon attack deals 2d6+attribute, using the higher of the two enhancement bonuses if one of your weapons has one. If wielding a rapier and dagger, it would be 1d8+1d4+attribute. This is exactly the same as a greatsword deals. After extra attack, you would make one weapon attack, one two weapon attack for a combined 3d6+2*attribute with shortswords, 1d6 less than a greatsword. If you have poisoned weapons or similar, this may be beneficial. Otherwise, greatswords and polearms deal more damage.
Two-Weapon Fighting Style.
Two-weapon fighting no longer requires that both weapons have the light property. When wielding two weapons, you strike with whichever hand has the better angle of attack, gaining a +1 bonus to weapon attack rolls.
Dual Wielder Feat.
Once on your turn, when you take the attack action and are two-weapon fighting, you may make one attack as a bonus action.
While two-weapon fighting, you may make a two-weapon attack in place of a reaction weapon attack, such as an opportunity attack.
You gain +1 to AC.
Natural Weapons and Two-Weapon Fighting. A character attacks with natural weapons as if he were dual wielding.
Multiple Arms. A character with multiple arms can add each additional arm’s attack to a two-weapon strike.
For example, Norman is a four-armed, dual-wielding, natural weapon using fighter with two scimitars and two bear claws. He has the Extra Attack (2) feature from the Fighter. On his turn, he makes one multiple-arm two-weapon strike. He rolls one attack with his highest attack roll with modifiers. If he hits, his attack deals his primary weapon’s damage, plus his off-hand, plus his bear claws’ damage. Norman’s two-weapon strike would deal 2d6 + Strength + 2d4 damage + any attack riders. On a critical hit, all of this damage is doubled. His secondary and tertiary attack can be used to attack with any of his weapons that he wants to attack with. In addition, if Norman has the Dual Wielder Feat, he can use a bonus action to attack again.
*NOTE: In my house rules, scimitars deal 1d8 damage, so Norman would deal 2d8 + Strength + 2d4 + attack riders.