Slitherine

There's been talk, both ehre and on the Steam forums of some sort of 'scoring graph' or the like that you can see. Just how do you get to it? I can't seem to find any button that works on the UI that brings me to these overview areas.

Also, speaking of score and the like, mostly for my own personal reference, but is there some sort of hall of fame that you can access, like in Civilization, or is there no record of your play history anywhere?

I've only seen these Graphs once the game was either won or lost. In the victory/loss-menu there is a tab where you can access them.
I guess it should not be there during the game to not break immersion of the uncertainty how strong your opponents really are.

A record of your play-history would be a neat feature. I don't think there's something like that implemented right now.

You can access the graphs when you won/lost or as observer when typing /score into the chat window. Active players can't access them. The reason given by the devs is that it would be too easy to see from the points when and what units someone built and so on.