With the military governing the Arab world's most populous nation, people around the world are wondering just how exactly Egypt got to the point where the entire government lost any legitimacy whatsoever. The answer, politically and militarily, goes back almost 60 years to the 1952 Free Officers' Revolution and the military coup that overthrew King Farouk and established a "republic" (in theory) in Egypt. All of Egypt's current problems, and its latest revolution, can be traced back to one man: Gamal Abdel Nasser, the Arab Republic of Egypt's first "president."
Nasser was one of the most successful dictators in the history of the postwar Middle East and almost every social and political problem in the country can be directly or indirectly traced back to the legacy of the man Egyptians called "El Reis" ("The Boss").
Egypt's four primary problems are basically the same as the rest of the Arab world suffers from. In all these nations you have political repression and torture, massive corruption, widespread poverty, and incompetent leadership. However, Egypt is the Arab world's superpower, and anything that happens there directly or indirectly affects the rest of the Middle East.
Incompetent leadership has often manifested its worst, and most politically damaging, aspects in Arab militaries. During Nasser's rule, 1952 until his death in 1970, the quality of the Egyptian armed forces declined sharply, as the four major problems grew rapidly. Within the Egyptian armed forces, Nasser's tenure saw crippling cronyism and petty factionalism. This sort of thing was common in Arab states, but in this case damaging what was potentially the most powerful of the frontline Arab states. This contributed greatly to Egypt's defeats in 1956 and 1967 against Israel. The shortcomings of the Egyptian officer corps made fighting any kind of successful military campaign all but impossible. Prior to the Six Day War in 1967, Egyptian officers treated their profession as more of a social club rather than a serious technical and leadership vocation. Egyptian Army officers often worked only 3-4 days a week, starting on Tuesdays and often leaving on Thursdays to attend to social events, drinking, and sports. The officer corps treated the Egyptian enlisted men very poorly, contributing in turn to very low morale among the troops.
During the 1967 Sinai campaign, the consequences of this neglect, and Nasser's failure to rectify it, became obvious when officers fled their positions before the Israeli armored forces actually attacked, leaving their men to be captured wholesale by Israeli troops. After 1967, dubbed "El Nabka" ("The Catastrophe") by Nasser, the leadership and training situation in the armed forces improved, but only after his death in 1970.
After Nasser died, and aided by massive injections of Soviet arms and military equipment, Egypt began to prepare for its next confrontation with Israel, under the leadership of its new president, Anwar Sadat. Despite having been Nasser's Vice President, Sadat was an infinitely better leader. Thanks in no small part to his Army Chief of Staff, General Sa'ad El Shazly, the Egyptian Army was able to improve the quality of its leadership, its infantry, anti-armor, and mechanized training, and mold itself into the best field army Egypt had ever deployed.
But the amount of damage done to the officer corps during Nasser's rule was almost incalculable, with leadership becoming worse the higher up the chain of command you went. A shining example would be Field Marshal Abdel Hakim Amer, Nasser's Deputy Supreme Commander and the commander of the Egyptian Army during the 1956 Suez War, the Yemeni Civil War, and the 1967 Six Day War. An alcoholic and a drug addict, Amer was a close personal friend of Nasser and simultaneously a major rival for control of Egypt. After the disaster of the Six Day War, Nasser needed a someone to blame for the Egyptian military's (and his own) failure. Amer was arrested and court-marshaled for treason along with 50 other officers, and was either murdered or committed suicide.
The Egyptian military recovered after Nasser's death, but not the rest of the country. While the military improved in quality, the government bureaucracy crumbled, with connections or juice (known in Arabic as "wasta") becoming the main means of getting the government to function. Without wasta, people couldn't get a job, or government services of any consequence.
Corruption, which exploded under Nasser, and continued to fester in the government under Sadat, simply increased exponentially under Hosni Mubarak's presidency. While Nasser's status as a leader of the Pan-Arabist movement and personal charisma ensured his continuing popularity, Mubarak possessed nothing to mask the rot that was infecting the country.
Nasser's greatest legacy, and one practiced by all subsequent Egyptian presidents, was widespread political repression, backed up by a terrifying secret police presence. Because of this, it has always been the police and domestic intelligence agencies, rather than the armed forces (unlike Syria) that have maintained the government's grip on power. Nasser's personal and popular charismatic appeal led the Egyptians to forgive him all manner of sins, even the disaster of the Six Day War, so he was certainly forgiven his use of a large police force and secret service to monitor the country and ruthlessly arrest and torture any opposition. Both Sadat and Hosni Mubarak continued and increased this practice until 2011, when it simply ceased to work any longer.
This, in short, is how Egypt got to where it is today: a poverty-stricken, corrupt country with a legacy of authoritarian government and a well-respected military now in full control of the Arab world's leader. Many are hoping that the military will not continue the tradition of tyranny, and so far they seem to be playing fair.