Most of the commoner pigeons and doves eat seed and grain. There are others that eat different types of food and some that feed exclusively on fruit, but the seed and grain eaters are most common. A normal pigeon mix available from feed suppliers is adequate.
Pigeons and doves also eat oats, wheat, corn and peas. All will eat linseed, rape and niger. Some will eat white ant larvae, wood lice, worms and cleaned maggots. All need some sort of grit.