I use brushes for hand washing dishes etc. These are easy to rinse off, and don't collect dirt/bacteria like sponges. For stubborn deposits I keep some of the blue scotchbrite sponges around, and also find them useful for cleaning counters etc. After a few uses they generally get tossed. I've found that laundering them doesn't work real well, as the scubbing part of them tends to detach from the sponge part. I suppose a bleach solution would help to disinfect them but I use them so seldomly it seems like more bother than it's worth. I keep separate brushes for scrubbing the sink and chasing food particles into the disposer, washing dishes, and scrubbing veggies.
Most dishwashing takes place in the Bosch dishwasher. Usually the only stuff that gets handwashed are pots and pans and other items that aren't dishwasher safe and/or are too big for the DW, as well as the coffee pot filter holders etc. Occasionally the dw leaves a bowl, plate, or utensil with some cooked on particles and those get the brush or sponge scrubbing treatment.