- do the dishes [American English]
- do the washing-up [British English]
Cambridge Dictionaries Online - Cambridge University Press
noun [U] (US dishes)
the act of cleaning plates, pans, glasses, knives, forks' etc. after a meal, or the items needing to be washed:
You do the washing-up and I'll do the drying.
There's an enormous pile of washing-up in the sink.