Do insects breath?

Why can't insects grow much bigger?

Because they wouldn't be able to get enough oxygen.

Insects don't have lungs. In addition, their blood cannot carry oxygen around the body (it only carries nutrients and waste products). So, how do insects get their oxygen in?

Insects have tiny tubes called tracheae (plural form of trachea) distributed around the body. Parts of the body that requires more energy, like legs, have larger numbers of such tubes for obvious reasons. Trachae branch like trees; the smallest ramifications are called tracheoles (in lungs, similarly, there are Bronchi and Bronchioles).

Some very active insects, like the locusts, can make movements throughout the trachea in order to get more air in. It is arguable whether this can be considered as some sort of breathing.

Air penetrates the trachea by diffusion.

The length which air can travel quickly enough by diffusion, in such tiny tubes, is very limited. That is about 1 cm. So that is why insects cannot grow larger than a few centimeters across.

If insects were to become very large, they would have to develop lungs, gills or something else. However, that hasn't yet happened.

Crabs, are larger animals which but their looks seems to be inspired in insects, breathe using gills (as fish do). These are tissues which are kept moist and allow the oxygen to get across to the blood system.