List of Team Comps (VERY WIP, ANY EXTRA INFO IS WELCOMED)
So with the new champ select coming soon I figured that in some lobbies people would actually try to make a comp in pre-game. Only problem with that is some people aren't entirely sure what each one is, which champions to pick when playing said comp, etc. I know a list like this would help me out a ton back when I first started to learn about comps, so why not try and get it out there in the hope for it to reach others who might be in the same spot I was. The list isnt ranked in anyway, just in the order I thought of them. Dont hesitate to tell me if I made a mistake or left off a comp, or to suggest improvements. Im Silver 5 its pretty safe to say that I dont know everything about the game. My suggested picks for each comp are not by any means the only ones you can play, just the ones I think of when I think about said comp.
Pick
Description: A comp focused on eliminating 1 target at a time, generally by CCing and bursting to death an out of place enemy. Champions who work well in these kinds of comps have great cc abilities.
Examples of Good Picks:
Examples of Counter picks:

Splitpush
This comp focuses on getting ahead and using that lead to split push constantly during mid and late game. This comp is mostly made up of AD champions with huge snowball potential and good waveclear and/or duelist abilities, however their are a few AP and Tank champions that can be used in this comp as well.
Examples of Good Picks:
Example of Counter Picks: 
Global
This comp uses global abilities to control the map. Once they hit level 6, they basically have global pressure everywhere on the map with their ults and
summoner spell. A 1v1 fight top lane can quickly turn into a 1v2 - 1v5 in an instant. While almost any champion can be used in this comp due to Teleport, generally champions with global ult abilities work better because it is what they were made for. However, a good early game team can set this comp behind, because if they are behind there is less of a chance you will get of a tp/ult to becoming your way. Also Champions with strong disengage can leave a global comp out of luck with summoner spells and ultimates wasted, which have very long cooldowns
Examples of Good Picks:
Examples of Good Counterpicks:

Poke
This comp uses long ranged abilities to deal damage while remaining a distance away from the enemy team. They are weak to dives and hard engage, but strong against teams made up of mostly immobile and melee champions.
Examples of Good Picks:

Examples of Counter Picks:

Siege
This comp focuses on grouping up and using a mixture of zoning and pushing power to take towers by force. If Split Push and Poke comps had a child, this would be the result.
Examples of Good Picks:
Examples of Counter Picks:

Protect the Carry Comp
More commonly known as Protect the Kog'Maw, this comp involves keeping your 1-2 late game hypercarries alive. This comp can be very strong if the protected champion or champions get ahead, but is not going to win if the protected champion(s) dont get ahead.
Examples of Good Picks:
Examples of Counter Picks:

Dive
A dive comp is where 2-3 member of a team dive a cetain enemy champion under a turret or near other teamates. While this comp is good against squishyier teams, teams with more tanks or with multitarget or aoe CC will be more than happy to stop your dive and get a double kill.
Examples of Good Picks:
Examples of Counter Picks:

AOE
AOE(Area of effect) comps are comprised of AOE CC abilities in order to lockdown as many enemy champions as possible and then deal massive ammounts of damage. These comps rely on hard engage, and multiple forms of AOE CC.
Examples of Good Picks:
Examples of Counter Picks:

again, feel free to add extra information for me to use to update this list. Whether I missed some team comps or forgot some crucial information on some comps I have listed (which I probably did both).
are used to catch someone in small windows of mispositioning, then rotate to sieze an objective.
While its weaknesses aren't particularly exploitable, its advantages are mostly limited to its catch potential, and is very difficult to execute, especially in the late game