US Domestic, you are in radar contact pretty much all the time. Ultimately you can use your emergency authority to avoid flying through a thunderstorm but as a practical matter, ATC is kept very much in the loop and is the practical solution to all the problems.
Normally there is no problem, as they fully understand your need not to fly through the stuff. I've only had one actual conflict and it went like this: We were southeast bound, approaching the Coaldale VOR to join J-92 down over Las Vegas and there was a giant thunderstorm on that airway. By the time we turned the corner at OAL it was apparent that this monster was going to crowd us off the airway to the east and it was too late to turn back and circumnavigate it to the west and south sides. There was no way to avoid the red and purple areas of the cell without going into Tonopah Test Range airspace.
The captain was flying and he had me advise center that we had to deviate to the east. They said they could not approve that and to stay on the airway. The problem was that the testing of the F-117 fighters was being conducted then, out of the Tonopah Test Range and it was active at that moment. They could not see these stealth aircraft on their radar and could not guarantee our separation. The captain got on the radio and re-stated that he was going about ten miles east of the airway centerline.
Again the controller said he could not approve that. The captain again said that was what he was going to do. A different voice came up as "center" and said: "Immediate right turn, heading 240!" or some similar direction out of TTR airspace. The captain said: "Negative."
A few miles further on, we were clear of the cell and I told them we could accept a right turn. They gave us a vector back to rejoin J-92 and that was the end of it. Never heard anything more about it. We expected the letters to come in about six months alleging a violation but nothing ever happened.
I think everyone involved thought as we did. The risk of collision with one little fighter in a thousand cubic miles of air was one factor, the certainty of flying into a level 5 or 6 thunderstorm at 33000' was another. While it was kind of a bad deal for all of us to be in, we went with the vastly better odds. Someone agreed.
The big deal on thunderstorm avoidance in the continental US is probably when the Marfa line is really active; you can get a line of monster cells from west Texas all the way to the Canadian border near Lake Erie. Every east/west flight has to deal with these lines of thunderstorms and hundreds of us end up slipping through the same couple of holes. The talk is about where the soft spots are and the traffic does get bunched up in them. Under these conditions I really admire the guys in the ARTCCs. They do a fabulous job of getting us through without running a bunch of us together.
Happiness is not seeing another trite Ste. Maarten photo all week long.