Note that provinces hit by nuclear bombs get reduced to 0 IC permanently. While this is not historically realistic (in the game time period, the bombs were only big enough to rip the heart out of a city, not level entire provinces), it can be used strategically - by targetting your opponent's high-IC provinces you can partially cripple their economy permanently. In my last game (as USA, with late war entry and rushing nukes) I was able to drop 6 nukes early in 1944 - and used them on Japan's 6 highest IC provinces. Now they have nothing over 12, and about half their usual IC....
How to use: Pick a strat bomber unit (or other unit capable of carrying it, indicated by an atom logo, but I'll use an SB as example since it's historic), and go into the unit stats screen (the one where it lists off about 15 stats and has the strategic redeploy/upgrade buttons). Click on the atom logo, and it will light up, indicating that one is now loaded. Then assign the bomber to strategic bombing on the target province.