Slitherine

Hello - what does it mean when you see smoke over your city - like this? (Couldn't find the answer in the manual or a title search here.)

I think it is rubble indicating the degree of destruction.
Looking at the map, I guess this around Krywyj Rih/Kryvyi Rih, was destroyed a lot in reality...

I see - does it mean anything in the game (penalties, etc.) or is it just a visual effect? Does it go away by itself?

This is from Battlefield Europe, or?
I am not aware of any consequences in the game but McGuba (or Uhu) may know better...

Yes it is Battlefield Europe - I'll investigate more there - thanks!

It is indeed just a cosmetic/visual feature to indicate destruction. It usually happens after a successful Allied bombing raid or the Axis capture of a Soviet city. By the end of the war many cities all over Europe lay in ruins.