I think they have lungs. I think that because when my pet grasshopper breathes in and out you can see his abdomen expand and contract as like humans do. This is different from humans or mammals because the insects' lungs are a lot smaller than a mammmals and they breathe through holes in their abdomen. That is really neat. No they do not have lungs.
People use lungs to get oxygen, a bug gets their through their skin or hard shell.
Click on the pictures below. Some others guessed at the answer. But really it is not a heart like a heart you would find in humans, or a horse or a dog. This is mostly correct. Insects do not have blood vessels that go to their legs and antennae.