Iran currently has one of the world's most vibrant and interesting film cultures, with an output of films that is as deeply moral and humane as it is visually arresting. The following five Iranian directors have quite a bit to do with that! Although I've ranked them alphabetically rather than by my own preference, Abbas Kiarostami is definitely the most celebrated of the bunch.
Bahman Ghobadi (1968-) is an Iranian Kurd, and, like many of Iran's best directors, a member of the Iranian cinema's "new wave". The Ghobadi film I've chosen, Turtles Can Fly, is a poignant story about children living in a refugee camp on the border of Turkey and Iraq at the beginning of the Iraq war. See it and see a part of the world you've seen only on CNN through a much different lens.
Abbas Kiarostami (1940-) is Iran's most famous filmmaker. One of the giants of world cinema, his sometimes deceptively simple films are treats both thematically and aesthetically. Cinematic poetry that it wouldn't be wrong to call intensely spiritual. Although I prefer a few other Kiarostami films over it, I've chosen Taste of Cherry as the representative Kiarostami film because it's his most well-known work, illustrates his personal style well, and because the Criterion edition is great quality.
Majid Majidi (1959-) is the only Iranian director to ever be nominated for an Academy Award. Although his nominated film—and my pick—The Children of Heaven eventually lost the award to Roberto Benigni's Life Is Beautiful, it was a worthy nominee. Both tragic and joyful, it tells the story of a young brother and sister duo who hatch a plan to share a pair of shoes because they can't afford two.
Mohsen Makhmalbaf (1957-) is the most political of my five picks. Many of his films have been banned in his home country. He is, however, also a most-dedicated artist. To create Kandahar, my film pick, he travelled to Afghanistan while it was still under the rule of the Taliban and observed how life unfolded for the Afghanis. Although Kandahar is not as immediately accessible as, say, the works of Majidi, Makhmalbaf is an important figure whose films deserve to be more widely seen. His daughter makes films, too.
Jafar Panahi (1960-) is the second-most well-known Iranian filmmaker in the West, after Kiarostami. His films, and especially The White Balloon and Crimson & Gold, have won many festival awards over the last decade or so. I've chosen another film as my Panahi pick, however: his 2006 work Offside, about a group of Iranian girls who disguise themselves as boys to attend a World Cup qualifier.
I hope you take a look at some of these films and directors, and enrich your cinema viewing as well as your worldview!