Soaps kill by washing away the protective waxy coating of soft bodied insects, such as aphids and thrips, by entering the pest’s respiratory system and causing internal damage. Soaps are not as effective in controlling hard bodied insects such as beetles, wasps, bees and flies. This is why soaps are often considered environmentally friendly, as they
selectively kill many of the soft-bodied pests, but rarely bother hard bodied beneficials such as ladybug beetles and predaceous wasps.
Soap has zero residual value as an insecticide. It is only effective against insects that come into contact with the wet spray. Once the spray has dried, insects will not be harmed by walking over the residue.
Coverage is extremely important - spraying the upper leaf surface will miss many of these insects since they are often found under or within curled leaves. Drench your plants well!
I actually prefer soaps that are made from natural substances vs. petroleum by-products. These salts of fatty acids, from vegetable oils and fats, are what most soaps are made from. Oleic acid, found in olive oil, is the most common insecticidal fatty acid and many hand dishwashing liquid makers incorporate these same soaps in their products, regardless of whether or not they tout them as "all-natural".