Of course this is not my picture but can be found athttp://www.fs.fed.us/wildflowers/pollinators/pollinator-of-the-month/images/hawkmoths/eumorpha_typhon_lg.jpg This is the sphinx moth, hawk moth or sometimes we call them the hummingbird moth because they can pause in mid-air in front of a flower and sip up its nectar. However, my moth was gone as soon as I tried to get my camera. But the feds site will let me use their picture.
You will see them flying now, usually around dusk although they feed on the nectar of flowers and serve as very good pollinators, particularly of flowers with very long "throats". This is because their "tongue" is so long. But....there is a problem for gardeners.
This is the hornworm and it is the larva or immature (baby) of the sphinx/hawk/hummingbird moth. You will see them devouring grape leaves (one of their favorites), tomato leaves and other garden crops. They can be devastating this time of year and you might see them again in the fall.
It is your call but if you want to control these "caterpillars" or larvae then use Bt (Dipel or Thuricide) or Spinosad for organic control. It will not harm the adult moth but will help in controlling the eating by the larvae. This will of course prevent the larvae that you kill from becoming more moths.