The Japanese bettle, or Popillia japonica, is a nasty invasive species that has infested most of the Eastern United States after being first detected in New Jersey in 1916.
This beetle is often confused with a lady bug or lady beetle, the little red or pink and black dotted beetles living in your garden. I do not know why this is, but numerous people I've spoken to have been confused on this issue.
Japanese beetles are fairly large, as long as a quarter if not as wide, and have iridescent green or gold backs. They also fly extremely slow. Lady bugs are small, a little smaller than a dime, with red or pink backs and black dots. They fly quickly. Do not mistake these two creatures. Lady bugs are the most beneficial insect you can have in your garden, and Japanese beetles are probably the worst pest you can have. You want one, you want to kill the other.
Homeowners usually know they have Japanese beetles by the damage they cause. Japanese beetles eat leaf tissue but leave the veins intact so you end up with skeletonized leaves. They also do not care for variety in their diet, if they find a plant they like they will eat that plant and only that plant until it is no more. So your whole garden might look fine but one plant.
In my experience Japanese beetles tend to prefer plants with large leaves, such as hardy hibiscus or most especially grape vine. I assume that is because there is more area between the veins and so the beetle can more easily eat around them.
In addition to causing damage to leaves, the larval form of Japanese beetles, commonly called white grubs, damage turf grasses by feeding on roots. They also attract moles who eat them as a food source.
In short, these bugs suck.
Last summer I had quite a problem with beetles, both in the lawn and on my plants. To combat them in the lawn I put down some milky spore bacteria, which kills the larvae and can exist in the lawn for up to a decade after application. I do not measure grub frequency in my lawn as I cannot see underground, so I don't know how effective this ways.
To combat adult beetles I used some bug-in-a-bag traps. I looked at Lowes & Home Depot, Home Depot did not carry any, Lowes had 2 varieties. I tried both, both worked about the same and both killed a lot of beetles. Basically it is a bag with a tapered opening like many bug or fish traps, the bug flies in, but cannot fly out. As a lure they include a little box that smells like flowers, it really is quite pleasant. I must have killed a few hundred beetles between the two bags, I'm hoping I got them before they could breed and that is why I've been lucky this year.
One bit of advice about the bag traps though is that you do not want to place them near your prized plants. The lure really attracts the beetles and not all of them will be caught, so place it a ways away from whatever you don't want eaten.
Another method of control is simply squashing the beetles. They fly very slow and are not that perceptive. If you spot one on a leaf you can easily grab it and squash it, it is just one at a time but every little bit helps.
Also, for those who do not like killing, remember these bugs are an invasive species, they are not supposed to be in North America at all, and they're throwing our ecosystem out of balance.