We mostly share chores, same as when we were working, but I do most of the cooking and Mr D does all of the gardening. He will cook for himself if I eat out, and will cook for both of us if I am not available, but we both prefer my cooking, and I am happy to do it, so I usually do.
We each do our own washing and ironing, and are lucky enough to have a cleaner who mops floors and cleans the bathroom etc, so mostly it's just if we are having someone round that we need to do a quick spit and polish, which we do between us.
I do things like wash cushion covers and throws - that wouldn't cross his mind - and I am far more particular about wiping surfaces and sinks regularly, so I do things like that when I see they need it (in practice this is every time Mr D is supposed to have cleaned the kitchen
). I water indoor plants (again, he wouldn't think about it) make sure things that need it are charged up (we have a lot of rechargeable lamps, for instance) and generally make the place look nice. He used to do all the decorating, but these days we get people in, as I'm not keen on him being up ladders and doing close work for health-related reasons.
We split admin on the basis of who sorted out a particular bill first. We keep saying we should organise that better, as there is no rhyme or reason to how it is done, but we don't get round to it. I tend to be the one who books things and keeps the calendar updated, and I do the grocery shopping. If there were a leak or burst pipe he would deal with it - I wouldn't have a clue, embarrassingly. That's something I need to find out about as we get older.