How the write(), read() and getvalue() methods of Python io.BytesIO work?

The issue is that you are positioned at the end of the stream. Think of the position like a cursor. Once you have written b' world', your cursor is at the end of the stream. When you try to .read(), you are reading everything after the position of the cursor – which is nothing, so you get the empty bytestring.

To navigate around the stream you can use the .seek method:

>>> import io
>>> in_memory = io.BytesIO(b'hello', )
>>> in_memory.write(b' world')
>>> in_memory.seek(0)  # go to the start of the stream
>>> print(in_memory.read())
b' world'

Note that, just like a filestream in write ('w') mode, the initial bytes b'hello' have been overwritten by your writing of b' world'.

.getvalue() just returns the entire contents of the stream regardless of current position.