Lots and lots of people do web stuff in Python. There are a whole bunch of Python web frameworks like Django, Pylons, Flask, etc.
And there are big sites written in Python, too. Reddit, YouTube, some Google apps, Spotify, Netflix.
Rust is still a bit young, but also has several web frameworks like Rocket. No big case studies that I know of, but Rust still has many more fields of applications than PHP does.