Carcinogens, how do they work? The easiest carcinogenic thing for me to grasp is radiation, as it directly messes with DNA. Then it seems there are other compounds that simply mimic hormones, but these shouldn't necessarily cause cancer, right? Then there are things that can accelerate mitosis or mess with other processes, which can inadvertently mess with DNA. So my question is, in general, how many different flavors of carcinogens are there? I know there are a lot, but can someone list a good few? Maybe some examples? I'm most interested in how plastics and things like smoke cause cancer. I think a few examples would be best in aiding my understanding.
Thank you!
Edit: I also just realized this is the Chemistry Stack Exchange, I think I am more interested in the chemistry side of this question, but it might need to be migrated.
There are at least two different radiationless pathways to wreak havoc on the DNA:


intercalaction: compounds like benzo[a]yrene or ethidium molecules slide between DNA strands and cause transcription errors
alkylation: compounds like N-Nitroso-N-methylurea may transfer alkyl groups to nucleobases


But the list is by no means complete.