I removed a crop of aphids from my indoor chilli plants this afternoon. Anything indoors near an open window or door will attract aphids and as usual I'd failed to spot them until they had taken hold and were thick under each leaf.
Over the years I've tried various methods of getting rid of aphids. Soapy water in a spray bottle seems to be the most obvious solution, but I have trouble finding the correct ratio of washing up liquid to water. Too diluted and the aphids survive; too concentrated and it damages the plant. Plus, the chillies themselves are pretty much ripe and I've started picking them, I don't really want them covered in detergent.
Jekka McVicar (of Jekka's Herb Farm) recommends making up a garlic infusion and spraying that instead, but I haven't found that entirely satisfactory. The aphids make the leaves and stems sticky. The garlic solution also makes them sticky, which makes the plants quite unpleasant to handle. (I think you're supposed to use the garlic solution more as a preventative than a cure.)
What I do, and it seems to work, is to take the plants outside into the garden, turn the nozzle of the garden hose on to its fiercest, most powerful setting, and blast the plant with a laser-like jet of water. The plant invariably falls over, and this time leaves fell off (though the fruit stayed intact). Once I'm sure every inch of the plant has been squirted, I leave it to drip dry a bit, then bring it back indoors. I'm not sure if the aphids are drowned or blasted right off the plant, and I don't really care.
Obviously this wouldn't be any good for seedlings or anything fragile, but chilli plants seem to stand up to it remarkably well.