If you have a "reach" weapon in hand then your reach is 10ft. Opponents leaving your reach (moving more than 10ft away) provoke an attack of opportunity. Opponents moving around inside your reach (say from 5ft to 10ft) do not provoke an attack of opportunity.
Note that this only applies to melee weapons with the light keyword. With the Dual Weapon Wielder feat, it also applies to non-light melee weapons.
I'm considering also applying it to darts, on the idea that what the game calls a "dart" is more like a throwing dagger. Also, I think throwing two darts is cool. Damage-wise, dart and dagger are the same — 1d4 piercing damage, range 20/60, finesse.
I'm considering restricting it to weapons you are proficient in. It seems strange to allow dual wielding (something that is really difficult - go on, try it yourself) with a weapon that you don't already know how to use.
The errata document has clarified that unarmed attacks are not a weapon, thus feats and features do not work with it.
Everyone is proficient with unarmed combat. An unarmed blow might be a punch, a kick, an elbow strike, a head butt, or a hit with another part of the body. It does 1 + STR Mod bludgeoning damage if you are unarmoured or wearing light armour. It does 2 + STR Mod damage if you are wearing medium or heavy armour.
If you have a level in Monk, however, then unarmed combat is completely different. Monks specifically train in unarmed combat.
Using a Shove or a Shove Aside makes the place of an attack but it is not an attack - you are not making an attack roll. This means that it does not work with features like dual-wielding.
Hitting a foe with a shield is just the same as hitting them with other parts of your armour - it is an unarmed attack. A shield is a worn piece of gear, so it is not a weapon, improvised or not.
The Shield Master feat has a special Shield Bash, that can be used to knock foes prone using a Bonus Action.
Fleeing creatures might have advantage on saving throws. Attacks against them might have disadvantage.
Why? To make it actually possible to flee combat. I don't want you thinking that your characters have no option but to fight to the death.
http://www.madadventurers.com/angry-rants-overpowered-encounters/#more-8241