This is a bit of an unusual question, so I'll see what I can do to be as specific as possible.
What are some of the current (or at least most frequent uses) for HTTPservice? What kind of webAPIs do people typically use for it that aren't homemade? I was sort of disappointed when I found out so much of the roblox webAPI is restricted from httpservice.
In the case of Homemade APIs, what is a recommended method of hosting them? are there free sites that allow you to host programs online, or is it possible to host programs Peer-to-peer from your computer, straight to roblox through your internet connection? (I'm assuming the latter is not the case, because that would be a web request nightmare if your game ever got popular)
If I need to clarify the nature of my question, just leave a comment and I'll make edits. I'm not necessarily looking for tutorials on how to write the actual webcode... but I wouldn't refuse it as it might be good to have for future reference.

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whooooah this is quite complicated. Thank you for the answer tho! The video tutorial seems to have been removed, is there another recent one you can link? Otherwise, I'll see if I can find one myself.
Which API are you referring too?
TrelloAPI, I believe.
Hm.. I can't seem to find an updated video tutorial. The TrelloAPI is used a lot in application centers. Look up tutorials for applications centers. You should find some and you can learn the Trello API that way.