So, I've seen various discussions (mostly awhile ago) around these weapons.  What I'm discussing in our game is this:

1. Two-handed:  You get GWF, etc. for this fighting style which grants bonus/advantages when forgoing a shield and finesse options
2. Finesse: Allows you to go all-in on DEX which not only improves to hit, but initiative, AC, etc.
3. Ranged: You can get Sharpshooter which is in line with GWF
4. Versatile: Really doesn't grant anything unique

Why would I go option #4 unless I'm valuing roleplay/theme, etc. over the math?  I could get myself a Rapier + Shield and likely be a better Sword and Board than if I used a longsword.  What about the Dwarf Paladin using a battle axe + shield.  Anything I get with a shield, I could get with finesse, have a better AC and Initiative as well as DEX saving throw...

It feels like there should be a Versatile Weapon Fighting style and a feat of some kind.  Like:

• When wielding a versatile weapon in one hand and no other weapon in the other hand gain a +2 bonus to damage (similar to dueling)
• When wielding a versatile weapon in two-hands gain a +2 bonus to AC (for dropping the shield)

Note, that I haven't thought this through, just throwing something out for conversation's sake.  I'm not sure what actually makes sense, but it feels like a gap here.  Why use any of these weapons really other than thematically?

Most (all?) versatile weapons deal higher damage when used with both hands is all I can see. It is not nothin', but it ain't much for most builds. 

• When wielding a versatile weapon in one hand and no other weapon in the other hand gain a +2 bonus to damage (similar to dueling)

This is already true with versatile weapon.  Provide you are wielding it with one hand at the time and no other weapon. 

• When wielding a versatile weapon in two-hands gain a +2 bonus to AC (for dropping the shield)

The GWF applies it to the versatile weapon user as well, provided they attack using both hands at the time.  So player can can take Duel Wielder feat, and start off combat with a versatile weapon and light weapon with the Thrown property.  They get the +1 AC while wielding both weapons,  but on a turn can use the BA to throw the one weapon and then take the Attack action using two hands for melee attacks and benefit from GWF.  Then pull out another light weapon to gain your +1 to AC.  

The versatile weapon mainly allows a player to be creative with their off hand.  They can interact with objects, hold a focus to cast spells, and when needed turn a d8 attack into a d10.  

The real advantage of versatile weapons is when you're running a character who normally goes with a two-handed weapon and you find a magic longsword or warhammer.  They can keep up with the two-handed style while taking advantage of that weapon.

I am trying to wrap my head around rapier and shield....

Note that you already gain something from weilding a weapon two-handed - it makes it harder for attackers to disarm you (using the Diarm action, DMG ch.9).

Quote from CrizpyNutz >>

So, I've seen various discussions (mostly awhile ago) around these weapons.  What I'm discussing in our game is this:

1. Two-handed:  You get GWF, etc. for this fighting style which grants bonus/advantages when forgoing a shield and finesse options
2. Finesse: Allows you to go all-in on DEX which not only improves to hit, but initiative, AC, etc.
3. Ranged: You can get Sharpshooter which is in line with GWF
4. Versatile: Really doesn't grant anything unique

Why would I go option #4 unless I'm valuing roleplay/theme, etc. over the math?  I could get myself a Rapier + Shield and likely be a better Sword and Board than if I used a longsword.  What about the Dwarf Paladin using a battle axe + shield.  Anything I get with a shield, I could get with finesse, have a better AC and Initiative as well as DEX saving throw...

It feels like there should be a Versatile Weapon Fighting style and a feat of some kind.  Like:

• When wielding a versatile weapon in one hand and no other weapon in the other hand gain a +2 bonus to damage (similar to dueling)
• When wielding a versatile weapon in two-hands gain a +2 bonus to AC (for dropping the shield)

Note, that I haven't thought this through, just throwing something out for conversation's sake.  I'm not sure what actually makes sense, but it feels like a gap here.  Why use any of these weapons really other than thematically?

You use them currently because everything else is balanced around them.

Longswords do less damage because they can be paired with a shield, for better protection.  They don't do potential one shot damage to every level 1 character though.   Saying that a Longsword wielded in both hands has the potential for 1D10+13 at a +0 to hit at level 1, without a feat investment?  Thats's an average of 19 damage, assuming you hit.  At the low end?  It still one shots everything but a 16 CON Barbarian at level 1.  

I don't understand the concept behind it.  Why is this being looked at?  

LOL I just couldn't do it.  I'm using my Dwarf with a Battle Axe and Shield and took Shield Master.

Quote from Greenstone_Walker >>

Note that you already gain something from weilding a weapon two-handed - it makes it harder for attackers to disarm you (using the Diarm action, DMG ch.9).

True enough, but also true of the Great Axe where I would do more damage 2-handed, plus have the feats and fighting style to support it.  I know that there are benefits - versatility of choice and  ability to do decent damage with the ability to use a shield, or 2-handed, or two-weapons, or not.  It's nothing that serious, just something that felt like it is missing for this weapon/style choice not to always fall below more powerful options.  Maybe I'm wrong about it and not considering the full picture...just still kinda feels like there should be "something"....

Quote from CrizpyNutz >>

Quote from Greenstone_Walker >>

Note that you already gain something from weilding a weapon two-handed - it makes it harder for attackers to disarm you (using the Diarm action, DMG ch.9).

 

True enough, but also true of the Great Axe where I would do more damage 2-handed, plus have the feats and fighting style to support it.  I know that there are benefits - versatility of choice and  ability to do decent damage with the ability to use a shield, or 2-handed, or two-weapons, or not.  It's nothing that serious, just something that felt like it is missing for this weapon/style choice not to always fall below more powerful options.  Maybe I'm wrong about it and not considering the full picture...just still kinda feels like there should be "something"....

 I bet there are special builds available in the rules as written that versatile weapons shine, I haven't found it yet, as such I use them more for flavor than building a character around the weapon. Though in certain rare scenarios it would be fun if not very practical.

Versatile weapons are meant to be used as 1-handers.  They're good for either 1H + Shield or dual-wielding if you take the feat.

The fact that they can do a bit extra damage by switching to 2H is mostly useless but potentially useful in rare situations where somehow your shield becomes useless for whatever reason.  If you typically use a 1H and prioritize finding those as your best magical items, then swinging your 1d10 flametongue longsword (or whatever) is going to beat a crappy 1d12 greataxe

Quote from CrizpyNutz >>

1. Two-handed:  You get GWF, etc. for this fighting style which grants bonus/advantages when forgoing a shield and finesse options
2. Finesse: Allows you to go all-in on DEX which not only improves to hit, but initiative, AC, etc.
3. Ranged: You can get Sharpshooter which is in line with GWF
4. Versatile: Really doesn't grant anything unique

 Well yeah this looks great when you only mention the benefits:

1. Two-handed: You can't use a shield, many are heavy so small races can't use well
2. Finesse: Damage tops out at d8, and honestly should probably cap at d6 because rapier is too good not to use in many cases
3. Ranged: Disadvantage if anyone is near you, disadvantage on prone targets
4. Versatile: ???

Maybe they could do more to have some kind of versatile specialist fighting style, but that's not really an archetype that I know of and not all keywords need to be equal. These are just medium-sized weapons that can be used a couple ways. It means they don't need to make a unique two-handed d10 sword or axe.

Quote from Xeresia >>

I am trying to wrap my head around rapier and shield....

That's what Liam O'Brien's character Orym of the Air Ashari wields. Works well for him as a tank. 

The reason versatile weapons are used is because they're versatile. For example, if a spell needs somatic components you need a free hand to cast it. With a Versatile weapon you can gain the extra melee damage until you're ready to cast a spell and then switch (with no action economy cost) to one hand and cast a spell. When you're done casting the spell, you go back to two handed (again with no action economy cost) for the extra melee damage. That's the unique benefit they grant. 

Damage dealing meleers will usually go with Strength and heavy two handed weapons. Tanking meleers will go with Dexterity and finesse weapons for the extra AC. People who want to do both with use versatile weapons. If they usually want to tank then they use a longsword and a shield. If they want to do extra damage then they drop the shield and switch to two handed without having to spend anything to Use Object. 

Rapier and small shield (specific name is slipping my mind) is very common in mid-Ren western Europe (Northwestern Spain and Southeastern France, specifically). Elements of it later bled into the revival efforts of the late 1800's and early 1900's.

Twere the Olympics what killed that.

Quote from AEDorsay >>

Rapier and small shield (specific name is slipping my mind) is very common in mid-Ren western Europe (Northwestern Spain and Southeastern France, specifically).

 Buckler.  It's where the term "swashbuckler" comes from ("swash"meant swaggering around with a drawn sword).