How fast should a website load?

The title almost says it all. How fast should a website load?

Searching this question brings a lot of different stories (most around 2011). Here they say that 50% of the users expect that the site loads under 2 seconds and that users will leave the site if it takes 3 seconds or more. But on other sites they say it should be at most half a second.

What are the current expectations of the users? Are there any (recent) studies on the load time of a page? Or perhaps on the page size?

I know a site should be as fast as possible, are there any numbers (standards / guidelines)?