Easy way to see the requests QGIS makes to a remote server?

For QGIS 3.14 Pi and up

Just hit F12 and you will get the network logger panel (the QGIS Network Logger plugin is now integrated into QGIS core).

For QGIS 3.6 up to 3.14 Pi

For QGIS 3.6 and more recent versions, there is a useful plugin called QGIS Network Logger, developed by Richard Duivenvoorde.

It is much easier to check the requests sent out by QGIS (sent via the QgsNetworkAccessManager).

It seems there is no easy way to do this in QGis, so I solved it by adding a simple proxy, Python Logging Proxy which "does what it says on the can".

I modified the file LoggingProxyHTTPHandler.py to comment out line 105

print response.content

since I didn't need to see the "contents" of the images being sent back. Then to run the proxy all you do is

python ./proxy.py

And in QGis go to Settigns->Options->Network and turn on the use proxy for web access and fill in localhost and 8000 for the Host and Port.

Then every time QGis requests a WMTS (or other web image) you will see the request and the response in the terminal.