explain from where, why and when yescrypt

I was puzzled by this news entry: it just brought more questions to my mind than anything else. Another question I actually had was "what was it before anyways" and "how do I tell" what I'm using now, but I'm only answering the former ("SHA-512") and not the latter ($6$ is SHA-512 and $y$ is yescrypt).

I also considered linking to crypt(5) to clarify the latter, maybe that could be useful as well?