breaking codes in World War II - what did the Axis powers accomplish?

You often hear of the great work done at Bletchley Park and other places when the UK and the US (with some help from Polish work done before the war) decrypted most of the German and Japanese codes used during World War II.
What about codes used by other nations, e.g. Italy? Were those broken as well? And did the Axis powers manage to break any of the Allied codes? When I read about code-breaking, it seems like it was all done by the Allies.

I found a Wikipedia article saying that the Germans broke a few Allied codes but the Germans were handicapped because their efforts were split up amongst a variety of departments.

ETA: can’t seem to find much about any Japanese efforts at code-breaking.

I’ve read that the Italian codes were relatively secure. I don’t know if this reflects an inherent superiority in their methods or just a lower priority given to breaking their codes.

Ironically, this turned out to be only a minor problem for the allies. Most Italian military operations were performed with the Germans. And Germany insisted that all joint operations use German codes.

The most important success of Axis codebreakers was by B-Dienst, the principal German Navy codebreaking organization. Among other successes, their main contribution was breaking Naval Cypher No. 3, which the British Admiralty used to route convoys. This was an important factor in the U-Boat war. More on that here.

Don’t forget the Swedes, who tapped the German phone lines through Sweden and quickly cracked the Geheimfernschreiber/“Sturgeon” cipher, which allowed them access to pretty much all german communications through the northern countries between 1940-1943.