My coping tactic was selective parenting ... So I had a threshold for when I would get cross and when I'd "not notice" something. Feeding crisps to the bookshelf for eg, I'd ignore that. Pulling DVDs off shelf, emptying the saucepan cupboard (non dangerous, non naughty, just exploring type behaviour) I would just ignore. I would however impose the natural consequence of them having to help tidy up later, even if they only managed a few pans, I'd praise the helping. Otherwise I think you get into this constant battle of "no DD, oh no don't get that out Dd! DD we do NOT do that, no wait don't touch that" and it's relentless.
I took the stance that I needed them to listen to me and really get it when they had done something actually naughty or dangerous - scribbled on the wall, got some scissors, fiddled with the oven. They do grow out of the feeding crisps to bookshelf stuff anyway, and once they are a bit older even just 6 months down the line, the tantrums are less and you can explain to them that actually we don't do that because it makes a mess etc and they are more receptive to it. It's almost survival parenting to get through this tough terrible twos stage. Pick your battles.
I also used to refuse to shift if I was having five mins with a cuppa. I'd just go in a diff room, ignore the sounds of mayhem, take that much needed breather and then go back in feeling calmer and deal with whatever they'd done while I'd had those five mins. Usually again it was a case of "oh children, you have emptied a bag of flour on the floor! Right, here's the dustpan and brush, off you go" ... They'd not actually manage to clean it but they'd try and that got the message across.
Extreme distraction (suddenly at the top of your voice running round the room shouting "oooh a bear") or ignoring tend to be the most effective things for my two with tantrums. (DD had sensory related meltdowns so I used a mix of the two depending on scale of the meltdown). Mostly just get out the house, grit your teeth and know that it will pass.