The Pyodide project will give you a full, standard Python interpreter that runs in your browser and also give you access to the browsers Web APIs. Currently, Pyodide does not support threading or networking sockets. Python is also quite a bit slower to run in the browser, although it is usable for interactive exploration.
Anyway, this sounds like a really interesting project. I always thought the demos I used to see of Python running in Silverlight in the browser were cool. That project is basically dead at this point, but Pyodide sounds like a really interesting new hack at getting Python into the browser. Hopefully it will go somewhere.