Identify at least two modern nations that have a Shi'i majority or a significant Shi'i population.
Shi'i Muslims, though they are a minority of the 1.4 billion Muslims worldwide, nonetheless have a significant population of 150 - 200 million followers. The larger Sunni sect of Islam makes up approximately 80 - 85% of the total number of Muslims on Earth.
Iran is the only modern nation with an overwhelmingly dominant Shi'i majority, as 90 - 95% of the faithful in that country belong to that sect. Other countries with a majority Shi'i population include Iraq, Bahrain, and Azerbaijan, all with roughly 2/3 Shi'i Muslims. Pakistan, Lebanon, Kuwait and Yemen, meanwhile, have Shi'i populations in the 30 - 35% range.
As confrontation between Sunni and Shi'i is common, along with the accompanying mistrust, Iran does not get along well with its Saud neighbors, nor most of the rest of the Arab Muslim world. Iran has worked closely with the Shi'i population of Iraq, including shipping them weapons when the insurgency there was active against US forces.