Do you mean Muslims? They eat meat, vegetables, grains... the usual stuff. See "What do christians eat?"
Many Muslims adhere to dietary laws and methods of slaughter called dhabihah. Foods which are haraam (harmful) per the Qur'an are:
- Pork meat (i.e. flesh of pig) [Qur'an 2:173]. Pork may be eaten in any instance wherein it will save your life and there is no other sustenance.
- Blood [Qur'an 2:173].
- All carnivores and birds of prey.
- Animals slaughtered in the name of anyone but Allah. All that has been dedicated or offered in sacrifice to an idolatrous altar or saint or a person considered to be "divine". [Qur'an 2:173] [Qur'an 5:3]
- Carrion [Qur'an 2:173]
- An Animal that has been strangled, beaten (to death), killed by a fall, gored (to death), savaged by a beast of prey (except that which you may have slaughtered while it was still alive); [Qur'an 5:3].
- Food over which Allah's name is not pronounced. [Qur'an 6:121].
- Alcohol and other intoxicants. [Qur'an 5:90-91].