Much of the recent political history of Ethiopia is the history of Haile Selassie. Selassie, or "His Imperial Majesty Haile Selassie I, Conquering Lion of the Tribe of Judah, King of Kings of Ethiopia and Elect of God", was a fascinating figure. He became fascinating early on -- as Crown Prince he furthered the modernization of Ethiopia, distributed lions to Western European leaders, and adopted forty Armenian orphans following the Armenian genocide and had them trained to form a band.
He was crowned Emperor in 1930. He immediately moved toward liberal democracy, establishing Ethiopia's first written constitution and creating a bicameral legislature. Of course, Europe couldn't allow this to continue, and in 1935 Italy invaded. Selassie mobilized his army, famously reminding them that they were going to die anyway, probably of "cough or head-cold", and it was better to die fighting Italians. Italy's modern army had no trouble defeating Ethiopia, especially after they began using chemical weapons and targeting hospitals.
On May 5, 1936, Selassie fled to Geneva via Israel to plead for help from the League of Nations. His speech there is a famous event in Ethiopia, and Wikipedia describes it as "a speech often considered among the most stirring of the 20th century." He was named Time's Man of the Year (the first black guy to appear on the cover), but the League decided not to do anything to help. (This episode inspired the ineffectuality clause in the UN charter.)
Selassie spent five years in exile, mostly producing counter-propaganda to respond to the Italians' stream of regular propaganda. Italy responded by executing several of his family members, looting Ethiopia's churches, and stealing its monuments and obelisks. Finally, during WWII British forces liberated Ethiopia. Selassie returned to Addis exactly five years after he fled.
Restored to power, he continued democratic reforms. A new constitution in 1955 provided broader public participation. He also sent troops around the world to participate in UN peacekeeping missions, saying basically that it would have been nice if someone had done the same for Ethiopia in 1936. But dissatisfaction with his rule accumulated, and there were unsuccessful coups. Communism became popular. Severe famines in the 1970s caused further dissatisfaction, especially when it appeared that Selassie (by then in his 80s) was unaware of the magnitude of suffering.
Finally the military revolted over salary issues. Selassie promised a pay increase, but the Derg ("sixty"), a committee appointed to investigate their grievances and led by Mengistu Haile Mariam, instead staged a coup. They imprisoned Selassie, executed a bunch of people, and then executed him.
Or did they?
Before his coronation as Emperor, he was known as Ras ("Lord") Tafari. The Rastafari believe that God ("Jah") manifested as Jesus and gave the world his teachings, but they were corrupted, so God manifested as Haile Selassie to reform the world. God cannot die, so the alleged execution of Haile Selassie by the Derg must be a hoax; Selassie lives on in hiding and will reveal himself and redeem humanity.
Rastas divide the world into Zion (Ethiopia or possibly all of Africa) and Babylon (everywhere else, but especially the developed world). Babylon has revolted against God, but God will redeem humanity and create paradise on Earth in Zion. Rastafari has strong elements of Afrocentrism, teaching that history is the story of whites harming blacks. The Back to Africa movement is looked upon favorably (since it calls for a return of blacks to Zion), and Marcus Garvey is believed to have been a prophet. For some time there were elements of black supremacy in Rastafari, but they largely disappeared after Haile Selassie condemned racism in a speech to the United Nations.
Many Rastas believe in eternal life -- apparently Bob Marley refused to write a will when he was dying of cancer because that would be giving in to death. Some feel so strongly that they will avoid saying words with "die" or "death" in them, for instance substituting "livication" for "dedication". At the paradise that God will create in Zion, everyone will speak Amharic, the language of Ethiopia, and some Rastas study Amharic now. Rastas famously smoke marijuana in a ceremony called a "reasoning", where they discuss social and political issues. Many Rastas follow the kosher dietary restrictions of the Torah. Many prefer to avoid the word Rastafarianism because they believe they have evolved above "-isms".
You don't actually see many Rastafari in Ethiopia, at least as far as I could tell. I guess Jamaica's a bit more pleasant.