The active ingredient in bleach, sodium hypochlorite (NaOCl), has a few ways of killing off microbes. One method involves causing particular proteins in the microbes to unfold, preventing their normal function and eventually killing the bacteria. Alternatively, bleach can disrupt the membrane that forms the outer shell of a bacteria. Since most bacterial membranes are very similar, bleach is very effective against a whole host of different types of bacteria. The human body actually produces hypochlorous acid (HOCl) itself to combat bacterial infections.
Iodine is useful as a disinfectant that can kill a wide variety of pathogens.