These pretty blue green beetles can become quite a plague in some years, though they tend to be more of a pest of ornamentals than vegetables. They do eat some vegetable crops though, including strawberries, eggplant, pepper and potato. Fortunately for western gardeners they only occur east of the Mississippi river.
The easiest way to control Japanese Beetles is to physically remove the adults by knocking them into a bucket of soapy water (if there are a lot of them you might try laying down a sheet and shaking the plants). It is a good idea to remove any adults you see, as feeding beetles may send out signals that attract other beetles. If they become a real problem you could use floating row covers to keep them off your plants. Parasitic nematodes and Milky spore disease can be used to kill larvae in the ground, but they can fly well and may travel up to 5 miles. You might also use rotenone spray. Pheremone traps are sometimes promoted as a solution, but it’s been found that they commonly attract more beetles to the garden than they actually catch.
Steven Katovich, USDA Forest Service, Bugwood.org