An entry visa is required by everyone to visit Iraq, regardless of the purpose of travel. An Iraqi visa allows the holder to enter the country once in the three month period from the date of approval for a trip up to three months. Visas for religious tourism and general travel must be obtained prior to arrival, but if you're coming solely to visit the Kurdistan Region, you can get one at their airport.
Health and Safety
Without sugar coating it, political unrest is still rampant in Iraq, and travelers are often targets of kidnapping. Terrorist attacks also persist due to continued resistance against military occupation, the Iraqi government and US and UK forces. Sectarian and factional conflicts also cause armed violence and street warfare. Travel to this part of the Arab world is not advised by some governments.
However, Kurdistan Iraq (in the northern region) is far from the chaotic central and southern regions of the country. It is increasingly becoming a tourism hub thanks to numerous developments in the area. It is a reasonably safe place to explore, but things can turn sour quickly if you cross the border. Kurdish people are friendly to westerners as long as you avoid areas beyond the Kurdistan regional government control.
Medical facilities are limited so buy comprehensive travel insurance to cover evacuation in the event of an emergency. Cholera is a problem in some parts of the country, so vaccination against the disease and precautions for sourcing clean water should be taken. The heat can pose a threat so ensure you remain well hydrated.