It's all a theoretically discussion still as we haven't witness an all-out nuclear war yet.
Nobody really knows for sure other than it would be catastrophic on an unfathomable scale.
Extinction of humanity, questionable. Collapse of civilization, very likely.
My take on the least grim outcome: There won't be any real winners, just unluckly survivers in fast declining numbers due to radiation (both short and long term fallout), other sickness, starvation (nuclear winter and nuclear famine ) and lots of other nightmarish hardship for decades and even centuries to come.
To believe in less severe consequences is a fallacy in my opinion. Most likely it will be far worse than this.
Lots of academic papers on nuclear war out there in addition to the various wikipedia articles already mentioned.
Only a few outliers advocate that an all-out nuclear war can be won in any meaningful way.
*Note that I wrote an all-out nuclear war, not a limited nuclear war between two adversaries (which according to most simulations done never stay limited anyways).
Enough off-topic